diff --git a/compiler/chapter_3.md b/compiler/chapter_3.md
index 489f6ef..cf78579 100644
--- a/compiler/chapter_3.md
+++ b/compiler/chapter_3.md
@@ -39,6 +39,10 @@ type ExprKind =
     ;
 ```
 
+Both `Stmt` (statement) and `Expr` (expression) are polymorphic types, meaning an expression, for example, can be either an addition operation containing 2 inner expressions or an integer expression containing the integer value, etc. This can also be implemented with classes and sub classes.
+
+For both `Stmt` and `Expr` there's an error-kind. This makes the parser simpler, as we won't need to manage parsing failures differently than successful parslings.
+
 ## Consumer of lexer
 
 To start, we'll implement a `Parser` class, which for now is simply a consumer of a token iterater, meaning the lexer. In simple terms, whereas the lexer is a transformation from text to tokens, the parser is a transformation from token to an AST, except that the parser is not an iterator.
@@ -62,25 +66,106 @@ This implementation should look familiar compared to the lexer. We use the `curr
 
 Just as the lexer, we'll have a `.pos()` method, returning the current position.
 
+For convenience, although there are other ways of doing it, we'll implement another public method on `Lexer`, which will return the lexer's current position.
+
+```ts
+class Lexer {
+    // ...
+    public currentPos(): Pos { return this.pos(); }
+    // ...
+}
+```
+The reason, is that when the lexer has reached the end of the file, the `.next()` method will return `null` instead of a token with a position, meaning we won't get the position after the last token.
+
 ```ts
 class Parser {
     // ...
-    private pos(): Pos { return this.current().pos; }
+    private pos(): Pos {
+        if (this.done())
+            return this.lexer.currentPos();
+        return this.current().pos;
+    }
     // ...
 }
 ```
 
-The parser does not need to keep track of `index`, `line` and `col` as those are stored in the tokens.
+The parser does not need to keep track of `index`, `line` and `col` as those are stored in the tokens. The token's position is prefered to the lexer's.
 
 Also like the lexer, we'll have a `.test()` method in the parser, which will test for token type rather than strings or regex.
 
 ```ts
 class Parser {
     // ...
-    private test(type: string): bool { return this.current().type === type; }
+    private test(type: string): bool {
+        return !this.done() && this.current().type === type;
+    }
+    // ...
+}
+```
+
+When testing, we first check that we have not reach the end. Either we have to do that here, or the caller will have to write something like `!this.done() && this.test(...)`, and it's easy to do it here.
+
+We'll also want a method for reporting errors.
+
+```ts
+class Parser {
+    // ...
+    private report(pos: Pos, msg: string) {
+        console.log(`Parser: ${msg} at ${pos.line}:${pos.col}`);
+    }
     // ...
 }
 ```
 
 ## Operands
 
+Operands are the individual parts of an operation. For example, in the math expression `a + b`, (would be `+ a b` in the input language), `a` and `b` are the *operands*, while `+` is the *operator*. In the expression `a + b * c`, the operands are `a`, `b` and `c`. But in the expression `a * (b + c)`, the operands of the multiply operation are `a` and `(b + c)`. `(b + c)` is an operands, because it is enclosed on both sides. This is how we'll define operands.
+
+We'll make a public method in `Parser` called `parseOperand`.
+
+```ts
+class Parser {
+    // ...
+    public parseOperand(): Expr {
+        const pos = this.pos();
+        if (this.test("int")) {
+            const value = this.current().intValue;
+            this.step();
+            return { kind: { type: "int", value }, pos };
+        }
+        this.report(pos "expected expr");
+        this.step();
+        return { kind: { type: "error" }, pos };
+    }
+    // ...
+}
+```
+
+### Integer
+
+Parsing an integer is a 1:1 translation between the integer token and an integer expression.
+
+```ts
+type ExprKind =
+    // ...
+    | { type: "int", value: number }
+    // ...
+    ;
+```
+
+```ts
+class Parser {
+    // ...
+    public parseOperand(): Expr {
+        // ...
+        if (this.test("int")) {
+            const value = this.current().intValue;
+            this.step();
+            return { kind: { type: "int", value }, pos };
+        }
+        // ...
+    }
+    // ...
+}
+```
+