The Sonata is a genre you have already become familiar with. Like the concerto however, it is a genre that becomes more narrow in its focus as we move into the classical period. As you recall, a Baroque sonata could be written for a wide variety of instruments or combination of instruments. Of course the trio sonata was very popular and had a fairly standard group of instruments, but the sonata in general was quite a flexible genre in terms of instrumentation. By contrast, in the Classical era, a sonata is a piece for solo instrument, almost always solo piano, or a duet between piano and solo instrument, usually a violin or cello.
Early in the Classical era these duo sonatas were essentially a piece for solo instrument with piano accompaniment. By the end of the classical era duo sonatas by Mozart and Beethoven feature the stringed instrument and the piano as equal partners. Duo sonatas, however, were not the most widely-composed form of the genre. By far the most popular kind of sonata was the piano sonata, a piece in multiple movements for piano alone. The BBC provides a very brief summary of classical sonata information, including the most common structures of sonata movements, along with an introduction to the musical form that was always used in the first movement of a sonata. This form is known as sonata-allegro form or sometimes just sonata form. We’ll cover this form in more detail later, but this site provides a simple introduction to the concept.