This is an anime series spanning three seasons with Nodame Cantabile, Nodame Cantabile: Paris Chapter and Nodame Cantabile: Finale.

Megumi Noda or "Nodame" is a piano student at Momogaoka College of Music. As an extremely talented pianist who wants to be a preschool teacher, she prefers playing by ear rather than reading the music score. She is messy and disorganized, takes baths several days apart and loves to eat. Shinichi Chiaki is Momogaoka's top student. Born into a musical family, he is talented in piano and violin and has secret ambitions to become a conductor.
They meet by accident and Nodame quickly falls in love but it takes much longer for Chiaki to even begin to appreciate Nodame's unusual qualities. Along the way, their relationship causes them both to develop and grow and they meet some crazy people (like Masumi, Mine, and Stresemann) and make lasting friendships. Because of Nodame, Chiaki gets the opportunity to lead a student orchestra and begins to have a broader appreciation of people's musical abilities. Because of Chiaki, Nodame faces her fears and enters a piano competition. Opportunities open up as both begin taking risks, stretching themselves far more than they ever thought possible.

Source:Wikipedia