Even though "Sonata" form (or Sonata-allegro form) is the underlying structure of much great classical music, an understanding of it seems to elude many piano students. But it's really quite simple, and if you understand the principle, a lot of great pieces will come alive for you in a new way.
Read this story, which I've written in sonata form:
Meet Alice, she's energetic. Meet Fred, he's shy. They go on a date and have many wonderful adventures. Then they go out for coffee and recap their adventures.
Substitute "1st theme" and 2nd "theme" for Alice and Fred and "violá," you have sonata form, the basis of a great deal of music composed by Haydn, Mozart, and Beethoven. Alice and Fred's adventures correspond to the development section.
Now have a listen to the great pianist Daniel Barenboim play a famous Mozart piece composed in Sonata form.
(BTW - What I've explained above refers to the "textbook" definition of sonata form that is taught in most music theory books and classes. During the actual classical period from 1750 to around 1820, the concept was much more flexible than we now generally think of it.)
If you want to learn how to improvise classical music, check out my video course.