Having been given the opportunity to study in Paris, Noda accompanies Chiaki to Europe as he strives to become the accomplished conductor he always dreamt to be.
 
(Source: Anime News Network)

Shinichi Chiaki is a first class musician whose dream is to play among the elites in Europe. Coming from a distinguished family, he is an infamous perfectionist; not only is he highly critical of himself, but of others as well. The only thing stopping Chiaki from leaving for Europe is his fear of flying. As a result, he's grounded in Japan. 
During his 4th year at Japan's top music university, Chiaki happens to meet Noda Megumi; or as she refers to herself, Nodame. On the surface, she seems to be an unkempt girl with no direction in life. However, when Chiaki hears Nodame play the piano for the first time, he is in awe at the kind of music she plays. To Chiaki's dismay, Nodame moves into the apartment next to his and finds out that she is head over heels in love with him. 
Nodame Cantabile tells the story of Chiaki and Nodame, as they not only learn to deal with each other, but learn lessons from one another as they strive for the top of the musical world. 
[Written by MAL Rewrite]

DVD special episode taking place before Episode 1 of Finale that focuses on Miki Kiyora making it to the final round of a competition in Paris.
 
(Source: Wiki)

The son of a famous pianist, music student Shinichi Chiaki dreams of studying abroad and becoming a conductor like his mentor. Unfortunately, his fear of flying grounds his lofty plans! As he watches other classmates achieve what he has always wanted, Shinichi wonders if he should quit music altogether. Then one day he meets fellow student Megumi Noda, also known as Nodame. This oddball girl cannot cook, clean, or even read a music score, but she can play the piano in incomparable Cantabile style. And she teaches Chiaki something that he has forgotten: to enjoy his music, no matter where he is. 
 
(Source: Kodansha USA) 
 
Note: Includes four bonus chapters and the side story "NodaCan BS".

An OVA centering around the life of Yukihisa Matsuda in Paris with his jealousy of Chiaki who is now a successful conductor also working in Paris. 
(Source: Wikipedia)

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