In iTunes, pressing the maximize button do not maximize the window. Instead it places the iTunes in mini-player mode. To maximize the window you have to tap the Option button on keyboard and click the Maximize button. The following steps can be followed to directly maximize the iTunes window through the button of Maximize.
Close the iTunes application.
Launch terminal and type the following command in it: defaults write com.apple.iTunes zoom-to-window -bool YES
Launch iTunes. Click the maximize button and it will maximize the window.
Now you can directly maximize the iTunes window by clicking the maximize button.