How to make Toolbar not overlap other content in Android?

I am trying to develop an activity with a toolbar (the example is more or less taken from a tutorial), but the Toolbar always overlaps part of the other content. Here is a screenshot:

The blue toolbar overlaps some of the other content. I have tried to search for a similar question on SO but only found something unrelated. I also tried to change the order of some elements and replaced wrap_content <-> match_parent which at most worsens the layout.

I am sure I am missing something very fundamental, but I do not see what.

Code of activity_main.xml:

<?xml version="1.0" encoding="utf-8"?>
<android.support.design.widget.CoordinatorLayout
    xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:app="http://schemas.android.com/apk/res-auto"
    xmlns:tools="http://schemas.android.com/tools"
    android:layout_width="match_parent"
    android:layout_height="match_parent"
    android:fitsSystemWindows="true"
    tools:context=".MainActivity" >

    <android.support.design.widget.AppBarLayout
        android:layout_height="wrap_content"
        android:layout_width="match_parent"
        android:theme="@style/AppTheme.AppBarOverlay">

        <android.support.v7.widget.Toolbar android:id="@+id/toolbar"
            android:layout_width="match_parent"
            android:layout_height="?attr/actionBarSize"
            android:background="?attr/colorPrimary"/>

    </android.support.design.widget.AppBarLayout>

    <include layout="@layout/content_main" />

</android.support.design.widget.CoordinatorLayout>

Code of content_main.xml:

<?xml version="1.0" encoding="utf-8"?>
  <GridLayout
        xmlns:android="http://schemas.android.com/apk/res/android"

        android:layout_width="wrap_content"
        android:layout_height="match_parent"

        android:useDefaultMargins="true"
        android:alignmentMode="alignBounds"
        android:columnOrderPreserved="false"

        android:columnCount="4"
        >

    <TextView
            android:text="@string/MainTitle"
            android:textSize="32dip"
            android:layout_columnSpan="4"
            android:layout_gravity="center_horizontal"
            android:id="@+id/textView1"
            />

    <TextView
            android:text="You can configure email in just a few steps:"
            android:textSize="16dip"

            android:layout_columnSpan="4"
            android:layout_gravity="left"
            />

    <TextView
            android:text="Email address:"

            android:layout_gravity="right"
            />

    <EditText
            android:ems="10"
            />

    <TextView
            android:text="Password:"

            android:layout_column="0"
            android:layout_gravity="right"
            />

    <EditText
            android:ems="8"
            />

    <Space
            android:layout_row="4"
            android:layout_column="0"
            android:layout_columnSpan="3"
            android:layout_gravity="fill"
            />

    <Button
            android:text="Next"
            android:id="@+id/imageButton1"
            android:layout_row="5"
            android:layout_column="3"
            />
</GridLayout>