diff --git a/webseite/classes/SubjectData.php b/webseite/classes/SubjectData.php
index ad82c1e..180df3d 100644
--- a/webseite/classes/SubjectData.php
+++ b/webseite/classes/SubjectData.php
@@ -48,7 +48,7 @@ class SubjectData
      * Gibt alle Fächer als SubjectData Objekt zurück
      * @return array Alle Fächer als SubjectData
      */
-    public static function getAll() : array
+    public static function getAll(): array
     {
         $result = array();
 
@@ -60,7 +60,7 @@ class SubjectData
             }
 
             $subjectData = SubjectData::fromName($subjectName);
-            if(!isset($subjectData)) {
+            if (!isset($subjectData)) {
                 continue;
             }
 
@@ -75,7 +75,7 @@ class SubjectData
      * @param $subjectId string Die eindeutige ID des Faches
      * @return SubjectData|null Das Fach zu der ID oder null, wenn kein entsprechendes Fach gefunden wurde
      */
-    public static function fromName(string $subjectId) : SubjectData|null
+    public static function fromName(string $subjectId): SubjectData|null
     {
         $result = new SubjectData();
 
@@ -84,34 +84,37 @@ class SubjectData
         $subjectDirectory = "config/subjects/$subjectId";
         $filename = "$subjectDirectory/properties.json";
         $data = Util::parseJsonFromFile($filename);
+        if(!isset($data)) {
+            return null;
+        }
 
         $result->id = $subjectId;
 
-        if(isset($data->displayName)) {
+        if (isset($data->displayName)) {
             $result->displayName = $data->displayName;
         } else {
             return null;
         }
 
-        if(isset($data->description)) {
+        if (isset($data->description)) {
             $result->description = $data->description;
         } else {
             return null;
         }
 
-        if(isset($data->color)) {
+        if (isset($data->color)) {
             $result->color = $data->color;
         } else {
             return null;
         }
 
-        if(isset($data->buttonText)) {
+        if (isset($data->buttonText)) {
             $result->buttonText = $data->buttonText;
         } else {
             return null;
         }
 
-        if(isset($data->icon)) {
+        if (isset($data->icon)) {
             $result->icon = $data->icon;
         } else {
             return null;
diff --git a/webseite/classes/TopicData.php b/webseite/classes/TopicData.php
index 1fd8900..ea09195 100644
--- a/webseite/classes/TopicData.php
+++ b/webseite/classes/TopicData.php
@@ -39,7 +39,7 @@ class TopicData
     public array $files;
 
     /**
-     * @var string Der gesamte Erklärungstext zum Thema, enthält fertiges HTML
+     * @var string Der gesamte Erklärungstext zum Thema, enthält fertiges HTML und LATEX Formelsyntax für MathJax https://docs.mathjax.org/en/latest/basic/mathematics.html
      */
     public string $article;
 
@@ -48,7 +48,7 @@ class TopicData
      * @param $subjectId string Die ID des Faches
      * @return array Alle zugehörigen Themen als TopicData Objekte
      */
-    public static function getAll(string $subjectId) : array
+    public static function getAll(string $subjectId): array
     {
         $result = array();
 
@@ -59,7 +59,7 @@ class TopicData
                 continue;
             }
             $topicData = TopicData::fromName($subjectId, $topicName);
-            if(!isset($topicData)) {
+            if (!isset($topicData)) {
                 continue;
             }
 
@@ -82,47 +82,52 @@ class TopicData
         $subjectId = Util::removeIllegalCharacters($subjectId);
         $topicId = Util::removeIllegalCharacters($topicId);
 
-        $topicDirectory = "config/subjects/$subjectId/topics";
-        $filename = "$topicDirectory/$topicId/properties.json";
-        $data = Util::parseJsonFromFile($filename);
+        $topicsDirectory = "config/subjects/$subjectId/topics";
+        $topicDataDirectory = "$topicsDirectory/$topicId";
+        $data = Util::parseJsonFromFile("$topicDataDirectory/properties.json");
+        if(!isset($data)) {
+            return null;
+        }
 
         $result->id = $topicId;
         $result->subjectId = $subjectId;
 
-        if(isset($data->displayName)) {
+        if (isset($data->displayName)) {
             $result->displayName = $data->displayName;
         } else {
             return null;
         }
 
-        if(isset($data->icon)) {
+        if (isset($data->icon)) {
             $result->icon = $data->icon;
         } else {
             return null;
         }
 
-        if(isset($data->description)) {
+        if (isset($data->description)) {
             $result->description = $data->description;
         } else {
             return null;
         }
 
-        if(isset($data->relatedTopics)) {
+        if (isset($data->relatedTopics)) {
             $result->relatedTopics = $data->relatedTopics;
         } else {
             $result->relatedTopics = array();
         }
-        if(isset($data->files)) {
+        if (isset($data->files)) {
             $result->files = $data->files;
         } else {
             $result->files = array();
         }
 
-        if(isset($data->article)) {
-            $result->article = $data->article;
-        } else {
-            return null;
+        $article = Util::readFileContent("$topicDataDirectory/article.html");
+        if (!isset($article)) {
+            $article = "Kein Erklärtext vorhanden";
         }
+        $article = str_replace('$TOPICPATH', $topicDataDirectory, $article);
+
+        $result->article = $article;
 
         return $result;
     }
diff --git a/webseite/classes/Util.php b/webseite/classes/Util.php
index b9f3e07..0df7596 100644
--- a/webseite/classes/Util.php
+++ b/webseite/classes/Util.php
@@ -15,6 +15,24 @@ class Util
         return preg_replace("/[^a-zA-Z0-9_-]/", "", $string);
     }
 
+    static function readFileContent(string $filename): string|null
+    {
+        if (!file_exists($filename)) {
+            return null;
+        }
+        $file = fopen($filename, "r");
+        if (!$file) {
+            return null;
+        }
+        $fileContent = fread($file, filesize($filename));
+        if (!$fileContent) {
+            return null;
+        }
+        fclose($file);
+
+        return $fileContent;
+    }
+
     /**
      * Öffnet eine Datei und gibt JSON-Inhalte als Array zurück
      * @param string $filename Dateipfad
@@ -22,10 +40,10 @@ class Util
      */
     static function parseJsonFromFile(string $filename): mixed
     {
-        $file = fopen($filename, "r") or die("Unable to open file!");
-        $fileContent = fread($file, filesize($filename));
-        fclose($file);
-
-        return json_decode($fileContent);
+        $content = self::readFileContent($filename);
+        if(!isset($content)) {
+            return null;
+        }
+        return json_decode($content);
     }
 }
\ No newline at end of file
diff --git a/webseite/config/subjects/deutsch/topics/topic4/properties.json b/webseite/config/subjects/deutsch/topics/topic4/properties.json
index 426de26..75b608a 100644
--- a/webseite/config/subjects/deutsch/topics/topic4/properties.json
+++ b/webseite/config/subjects/deutsch/topics/topic4/properties.json
@@ -1,5 +1,5 @@
 {
-  "displayName": "Thema 1",
+  "displayName": "Thema 4",
   "icon": "fa-divide",
   "description": "Eine kurze Beschreibung des Themas",
   "relatedTopics": [
diff --git a/webseite/config/subjects/deutsch/topics/topic5/properties.json b/webseite/config/subjects/deutsch/topics/topic5/properties.json
index 426de26..5b0924d 100644
--- a/webseite/config/subjects/deutsch/topics/topic5/properties.json
+++ b/webseite/config/subjects/deutsch/topics/topic5/properties.json
@@ -1,5 +1,5 @@
 {
-  "displayName": "Thema 1",
+  "displayName": "Thema 5",
   "icon": "fa-divide",
   "description": "Eine kurze Beschreibung des Themas",
   "relatedTopics": [
diff --git a/webseite/config/subjects/deutsch/topics/topic6/properties.json b/webseite/config/subjects/deutsch/topics/topic6/properties.json
index 426de26..fade52f 100644
--- a/webseite/config/subjects/deutsch/topics/topic6/properties.json
+++ b/webseite/config/subjects/deutsch/topics/topic6/properties.json
@@ -1,5 +1,5 @@
 {
-  "displayName": "Thema 1",
+  "displayName": "Thema 6",
   "icon": "fa-divide",
   "description": "Eine kurze Beschreibung des Themas",
   "relatedTopics": [
diff --git a/webseite/config/subjects/deutsch/topics/topic7/properties.json b/webseite/config/subjects/deutsch/topics/topic7/properties.json
index 426de26..d6ad914 100644
--- a/webseite/config/subjects/deutsch/topics/topic7/properties.json
+++ b/webseite/config/subjects/deutsch/topics/topic7/properties.json
@@ -1,5 +1,5 @@
 {
-  "displayName": "Thema 1",
+  "displayName": "Thema 7",
   "icon": "fa-divide",
   "description": "Eine kurze Beschreibung des Themas",
   "relatedTopics": [
diff --git a/webseite/config/subjects/deutsch/topics/topic8/properties.json b/webseite/config/subjects/deutsch/topics/topic8/properties.json
index 426de26..22e4e58 100644
--- a/webseite/config/subjects/deutsch/topics/topic8/properties.json
+++ b/webseite/config/subjects/deutsch/topics/topic8/properties.json
@@ -1,5 +1,5 @@
 {
-  "displayName": "Thema 1",
+  "displayName": "Thema 8",
   "icon": "fa-divide",
   "description": "Eine kurze Beschreibung des Themas",
   "relatedTopics": [
diff --git a/webseite/config/subjects/mathe/topics/topic1/article.html b/webseite/config/subjects/mathe/topics/topic1/article.html
index e69de29..74f9470 100644
--- a/webseite/config/subjects/mathe/topics/topic1/article.html
+++ b/webseite/config/subjects/mathe/topics/topic1/article.html
@@ -0,0 +1,5 @@
+Das ist der Erklärtext
+<img alt="Ein Bild" src="$TOPICPATH/image.png">
+<br>
+When \(a \ne 0\), there are two solutions to \(ax^2 + bx + c = 0\) and they are
+$$x = {-b \pm \sqrt{b^2-4ac} \over 2a}.$$
\ No newline at end of file
diff --git a/webseite/config/subjects/mathe/topics/topic1/properties.json b/webseite/config/subjects/mathe/topics/topic1/properties.json
index 4b30111..426de26 100644
--- a/webseite/config/subjects/mathe/topics/topic1/properties.json
+++ b/webseite/config/subjects/mathe/topics/topic1/properties.json
@@ -7,6 +7,5 @@
   ],
   "files": [
     "exercise1.pdf"
-  ],
-  "article": "Eine lange Erklärung\n![Alt Text](image.png)"
+  ]
 }
\ No newline at end of file
diff --git a/webseite/config/subjects/mathe/topics/topic2/properties.json b/webseite/config/subjects/mathe/topics/topic2/properties.json
index 426de26..d776814 100644
--- a/webseite/config/subjects/mathe/topics/topic2/properties.json
+++ b/webseite/config/subjects/mathe/topics/topic2/properties.json
@@ -1,9 +1,9 @@
 {
-  "displayName": "Thema 1",
+  "displayName": "Thema 2",
   "icon": "fa-divide",
   "description": "Eine kurze Beschreibung des Themas",
   "relatedTopics": [
-    "topic2", "topic3"
+    "topic1", "topic3"
   ],
   "files": [
     "exercise1.pdf"
diff --git a/webseite/config/subjects/mathe/topics/topic3/properties.json b/webseite/config/subjects/mathe/topics/topic3/properties.json
index 426de26..cbe7e38 100644
--- a/webseite/config/subjects/mathe/topics/topic3/properties.json
+++ b/webseite/config/subjects/mathe/topics/topic3/properties.json
@@ -1,9 +1,9 @@
 {
-  "displayName": "Thema 1",
+  "displayName": "Thema 3",
   "icon": "fa-divide",
   "description": "Eine kurze Beschreibung des Themas",
   "relatedTopics": [
-    "topic2", "topic3"
+    "topic1", "topic2"
   ],
   "files": [
     "exercise1.pdf"
diff --git a/webseite/homepage.php b/webseite/homepage.php
index 9fb93ce..1f30b51 100644
--- a/webseite/homepage.php
+++ b/webseite/homepage.php
@@ -8,6 +8,7 @@
     <link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.0.0/css/all.min.css" rel="stylesheet">
     <script src="https://cdnjs.cloudflare.com/ajax/libs/gsap/3.12.2/gsap.min.js"></script>
     <script src="https://cdn.tailwindcss.com"></script>
+    <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
     <style>
         @keyframes float {
             0%, 100% { transform: translateY(0px); }
diff --git a/webseite/subject.php b/webseite/subject.php
index c3bdf71..5e74132 100644
--- a/webseite/subject.php
+++ b/webseite/subject.php
@@ -4,7 +4,13 @@
 require_once ("classes/SubjectData.php");
 require_once ("classes/TopicData.php");
 
+if(!isset($_GET["subject"])) {
+    die("Ungültige Seite");
+}
 $subjectData = SubjectData::fromName($_GET["subject"]);
+if(!isset($subjectData)) {
+    die("Ungültige Seite");
+}
 $topics = $subjectData->topics;
 ?>
 
@@ -15,6 +21,7 @@ $topics = $subjectData->topics;
     <meta name="viewport" content="width=device-width, initial-scale=1.0">
     <title><?php echo($subjectData->displayName); ?> 5. Klasse - Modern</title>
     <link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.0.0/css/all.min.css" rel="stylesheet">
+    <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
     <style>
         * {
             margin: 0;
@@ -536,23 +543,23 @@ $topics = $subjectData->topics;
 
         <?php
 
-        foreach ($topics as $topic) {
+        foreach ($topics as $topicData) {
             ?>
 
-            <div class="topic-card" onclick="window.location.href='topic.php?subject=<?php echo($topic->subjectId); ?>&topic=<?php echo($topic->id); ?>'" style="cursor: pointer;">
+            <div class="topic-card" onclick="window.location.href='topic.php?subject=<?php echo($topicData->subjectId); ?>&topic=<?php echo($topicData->id); ?>'" style="cursor: pointer;">
                 <div class="topic-header">
-                    <i class="fas <?php echo($topic->icon); ?> topic-icon"></i>
-                    <h3 class="topic-title"><?php echo($topic->displayName); ?></h3>
+                    <i class="fas <?php echo($topicData->icon); ?> topic-icon"></i>
+                    <h3 class="topic-title"><?php echo($topicData->displayName); ?></h3>
                 </div>
                 <div class="topic-content">
                     <p class="topic-description">
-                        <?php echo($topic->description); ?>
+                        <?php echo($topicData->description); ?>
                     </p>
                     <div class="related-topics">
                         <h4>Verwandte Themen:</h4>
                         <ul>
                             <?php
-                                foreach ($topic->relatedTopics as $relatedTopic) {
+                                foreach ($topicData->relatedTopics as $relatedTopic) {
                                     ?>
 
                                     <li><?php echo($relatedTopic); ?></li>
@@ -567,28 +574,18 @@ $topics = $subjectData->topics;
                     <h4>Übungen herunterladen:</h4>
                     <div class="download-links">
                         <?php
-                            foreach ($topic->files as $file) {
+                            foreach ($topicData->files as $fileName) {
                                 ?>
 
 
-                                <a href="#" class="download-btn">
+                                <a href="<?php echo("config/subjects/$subjectData->id/topics/$topicData->id/$fileName")?>" target="_blank" class="download-btn">
                                     <i class="fas fa-file-pdf"></i>
-                                    <?php echo($file); ?>
+                                    <?php echo($fileName); ?>
                                 </a>
 
                                 <?php
                             }
                         ?>
-
-
-                        <a href="#" class="download-btn">
-                            <i class="fas fa-file-pdf"></i>
-                            Übung 1
-                        </a>
-                        <a href="#" class="download-btn">
-                            <i class="fas fa-file-pdf"></i>
-                            Übung 2
-                        </a>
                     </div>
                 </div>
                 <div class="progress-bar" data-progress="100">
diff --git a/webseite/topic.php b/webseite/topic.php
index 7cf77e7..bc93bb3 100644
--- a/webseite/topic.php
+++ b/webseite/topic.php
@@ -4,8 +4,20 @@
 require_once ("classes/SubjectData.php");
 require_once ("classes/TopicData.php");
 
+if(!isset($_GET["subject"])) {
+    die("Ungültige Seite");
+}
 $subjectData = SubjectData::fromName($_GET["subject"]);
+if(!isset($subjectData)) {
+    die("Ungültige Seite");
+}
+if(!isset($_GET["topic"])) {
+    die("Ungültige Seite");
+}
 $topicData = TopicData::fromName($_GET["subject"], $_GET["topic"]);
+if(!isset($topicData)) {
+    die("Ungültige Seite");
+}
 
 ?>
 
@@ -16,6 +28,7 @@ $topicData = TopicData::fromName($_GET["subject"], $_GET["topic"]);
     <title><?php echo($topicData->displayName); ?> - <?php echo($subjectData->displayName); ?></title>
     <link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.0.0/css/all.min.css" rel="stylesheet">
     <script src="https://cdnjs.cloudflare.com/ajax/libs/gsap/3.12.2/gsap.min.js"></script>
+    <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
     <style>
         * {
             margin: 0;
@@ -330,7 +343,7 @@ $topicData = TopicData::fromName($_GET["subject"], $_GET["topic"]);
         <p class="content-text">
             <?php echo($topicData->description); ?>
         </p>
-        <p class="content-text">
+        <p class="content-text article-section">
             <?php echo($topicData->article); ?>
         </p>
 
@@ -338,12 +351,12 @@ $topicData = TopicData::fromName($_GET["subject"], $_GET["topic"]);
             <h3 style="margin-bottom: 1rem;">Übungen herunterladen:</h3>
             <div style="display: flex; flex-wrap: wrap; gap: 0.5rem;">
                 <?php
-                foreach ($topicData->files as $file) {
+                foreach ($topicData->files as $fileName) {
                     ?>
 
-                    <a href="#" class="download-btn">
+                    <a href='<?php echo("config/subjects/$subjectData->id/topics/$topicData->id/$fileName")?>' target="_blank" class="download-btn">
                         <i class="fas fa-file-pdf"></i>
-                        <?php echo($file); ?>
+                        <?php echo($fileName); ?>
                     </a>
 
                     <?php
@@ -363,7 +376,9 @@ $topicData = TopicData::fromName($_GET["subject"], $_GET["topic"]);
             foreach ($topicData->relatedTopics as $relatedTopic) {
                 ?>
 
-                <span class="topic-tag"><?php echo($relatedTopic); ?></span>
+                <a href='<?php echo("topic.php?subject=$subjectData->id&topic=$relatedTopic") ?>'>
+                    <span class="topic-tag"><?php echo($relatedTopic); ?></span>
+                </a>
 
                 <?php
             }