What you are seeing in white is the re-size border. You can remove that and still make the window resizable by setting ResizeMode="CanResizeWithGrip" AllowsTransparency="True"
If you dont want to resize at all then do this – ResizeMode="NoResize"
, again you wont see the border but you cant resize.
<Window x:Class="HandsOnSolution.MainWindow"
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
Title="MainWindow" Height="350" Width="525" Background="Green" WindowStyle="None" ResizeMode="CanResizeWithGrip" AllowsTransparency="True">
<Grid>
</Grid>
</Window>
Edit
Good point by @devuxer, if you are interested in dragging you can add this piece of code to the window mouse down event
<Window MouseLeftButtonDown="Window_MouseLeftButtonDown"/>
//code behind
private void Window_MouseLeftButtonDown(object sender, MouseButtonEventArgs e)
{
DragMove();
}