Piano Sonata No. 31 in A-flat major, Op. 110, is a composition by Ludwig van Beethoven, completed in 1821. It is one of his late piano sonatas, showcasing his innovative style and emotional depth. The sonata consists of three movements, each with distinct character and complexity, reflecting Beethoven's mastery of form and expression. The first movement is marked by lyrical themes and contrasts, while the second movement features a lively fugue. The final movement is particularly notable for its introspective and spiritual qualities, culminating in a powerful conclusion that highlights Beethoven's profound musical language and personal struggles.