So, one of the first things to realize about Moonlight Sonata is that the “nickname” is a little bit misleading. Poet Heinrich Rellstab wrote that the first movement reminded him of moonlight on Lake Lucerne. The “moonlight” nickname is somewhat of a misnomer for a movement that has the character of a funeral march.
This video, by and far, is one of the most useful resources out there for understanding the harmonic structure of the Moonlight Sonata.
However, be careful of the i4/2 chord in the second measure of the piece. The descending “B” in the left hand is merely a passing tone. If we understand the first two measures as an expansion of the c# minor harmony, we are more inclined to bring that “B” pitch out in the left hand. Another nice feature of this piece is the D-major Neapolitan event in m. 3 which prepares for the arrival of the dominant harmony in m. 4. Understanding these opening measures as an introduction helps the performer and listener appreciate the first movement of the Moonlight Sonata as an approximate truncated sonata form.
The first movement has somewhat of a “funeral march” feel to it. Czerny commented on a “nocturnal feel,” which is somewhat misleading when referencing the late nineteenth century “nocturne” genre pioneered by John Field and refined by Chopin.
The other movements of this piece are also performance forces to be reckoned with. Movement 2, a scherzo and trio, is in D-flat major, which is the enharmonic equivalent of C-sharp minor. The third movement, a fast Presto agitato, is in sonata form. It is also important to point out that the most important movement of the entire sonata is that last movement. In some senses, Beethoven has created a tier of difficult in performing all three movements of the piece. Movement I is relatively easy, while Movement II is slightly more difficult. Finally, Movement III is incredibly difficult to play. In some senses, Movement III is a “composing out” of the motivic material found in Movement I.