How many movements are in a classical concerto and sonata? What are the forms for each movement?

Answer 1

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Answer 2

Moonlight Sonata has 3.  The first one is slow.  The 3rd one is fast.

Answer 3

Concerto (usually) has 3 movements, 1st and 3rd are fast (allegro or presto), with a slow movement (adagio or largo) in between.

Sonata may have 2-4 movements. This changed over time but since the early 19th century, a 4-movement form has been the most common.

A 1st movement is usually a Sonata-Allegro form - there is an exposition, a development, a recap, and coda.

2nd movement is a slow form, adagio or largo.

A 3rd movement is a dance form usually in a triple metre - a minuet or scherzo for example.

The 4th movement is another faster part, a Sonata-Allegro or a Rondo.

Edit:

Moonlight Sonata (op.27 No.2) is an exception. Another sonata, No.1 from this opus also has a slow 1st and faster 2nd movement. Critics think in this opus Bethoveen rebelled against conventional order, because he wanted to build the sonata from prelude towards the grand finale. A fast 1st movement would determine the character of the piece from the very start.