Hello!
In honor of the new user (Dmitri), I'll make a list of some Shostakovich pieces that are among my favorites.
(Just some foreshadowing if you decide to listen to these, most of his pieces are pretty difficult to listen to)
Shostakovich Piano concerto no. 2, 2nd movement: A break from his usual style, this is an incredibly underappreciated pieces, it's one of the most calming I've ever heard.
Shostakovich String quartet no. 8 in C minor: possibly his most famous, it is believed that he wrote this in 3 days, it was also disputed that he wrote it as a s_____e note.
Shostakovich cello concerto no. 2: the entire thing is very slow, but very good, he dedicated it to Rostropovich (a famous cellist from the time) and it is known as a very difficult piece, it also depicts a story (which you can look up).
Shostakovich String quartet no. 9, 5th movement: (I was just listening to this one today!) Also very distressing and very interesting, he uses a multitude of col legno on the body of the instrument, and it's a very interesting listen.
Shostakovich symphony no. 5: very famous, it is a staple in Russian music, and has many extremes, would recommend.
Shostakovich symphony no. 15: not so famous but equally as entertaining, this piece contains a multitude of quotes from other compositions, try to find them all!
I know I haven't got them all (I'm still just exploring music), but add any other of his compositions if you think they should deserve to be here too.