added comments on the methods & classes

src/Application.java

@@ -3,9 +3,13 @@ import java.util.List;
 
 public class Application {
     public static void main(String[] args) {
+        //List with a fitting String to be parsed into multiple tokens
         List<String> test = Arrays.asList("1 + xy^2 - (31 * x)y");
+        //Iterates through every String
         for (String value: test) {
+            //creates a list of tokens out of the String
             List<Lexer.Token> tokens = Lexer.lex(value);
+            //prints each token out (with .toString())
             for(Lexer.Token singleToken: tokens) {
                 System.out.println(singleToken.toString());
             }

src/Lexer.java

@@ -2,10 +2,14 @@ import java.util.LinkedList;
 import java.util.List;
 
 public class Lexer {
+
+    //enum TokenType that can either be a number, variable or a special character (like * or / etc.)
     public static enum TokenType {
         NUMBER, VARIABLE, SPECIAL
     }
 
+    //tokens with a TokenType that represents their type and a String with the actual data
+    //has for both values a getter method and overrides toString with it's fitting values
     public static class Token {
         protected TokenType type;
         protected String data;
@@ -28,11 +32,16 @@ public class Lexer {
         }
     }
 
+    //creates a list of tokens from a given String
     public static List<Token> lex(String input) {
+        //the list that will be returned at the end
         List<Token> result = new LinkedList<Token>();
+        //for-loop that iterates through each character of the String
         for(int index=0; index < input.length();) {
 
             char current = input.charAt(index);
+            //checks if a character is a digit, then creates a token with one or multiple numbers
+            //with TokenType=NUMBER
             if(Character.isDigit(current)) {
                 int endIndex = index+1;
                 if(endIndex<input.length()) {
@@ -44,9 +53,8 @@ public class Lexer {
                 result.add(token);
                 index += endIndex - index;
             }
-            else if(Character.isWhitespace(current)) {
-                index++;
-            }
+            //checks if a character is a letter, then creates for each following character a separate token
+            //with TokenType=VARIABLE
             else if(Character.isLetter(current)){
                 int iterator = index;
                 while(Character.isLetter(input.charAt(iterator)) && iterator<input.length()) {
@@ -59,6 +67,12 @@ public class Lexer {
                 }
                 index += iterator - index;
             }
+            //whitespaces are ignored
+            else if(Character.isWhitespace(current)) {
+                index++;
+            }
+            //every char of the string that isn't a digit, letter or whitespace will be
+            //used for creating a token with TokenType=SPECIAL
             else {
                 Token token = new Token(TokenType.SPECIAL, String.valueOf(current));
                 result.add(token);