This Adagio by Pyotr Ilyich Tchaikovsky (same as Tchaikovsky) is a deeply expressive and melancholic piece, known for its rich harmonies and poignant melodic content.
Emphasize the importance of sustained tone and emotional depth in shaping the melodic contours.
Adagio in C major is rated Henle level 5 of 9 — late intermediate repertoire, roughly ABRSM grades 6–7.
You should be comfortable at Henle level 5 — meaning you can already play level 4–5 pieces cleanly. Learning it one level early is possible as a stretch piece, but more than that usually leads to months of frustration.
Adagio in C major is available as free public-domain sheet music on IMSLP — the score is linked directly from this page.