This is a pretty great collection of selected short stories from Chekhov, plus two plays (one major, one minor) and a few letters. I am not a man who cares about an author's letters, so I won't be discussing those.
Chekhov helped set the standard for the short story - you might say he invented the 'modern' short story - and this collection gives you a good idea of how. Before Chekhov, stories were always concerned with Plot (with a capital P) - i.e. the only thing that mattered was narrative. Chekhov introduced a greater focus on character and nuance. It is hard to imagine the shorty story - particularly the American short story - or what we might call "European" cinema without him and his emphasis on character and tone over narrative. One comparison I could make is that Chekhov is to the short story tradition (and, perhaps, fiction as a whole) as Debussy and Satie are to "classical" music. (If that sounds like high praise, it's meant that way.) This collection lets us see that.
There is no way I will ever make my way through all of Chekhov's hundreds of stories but this collection gives me a sense of Chekhov as a writer.
On the other hand, only one of Chekhov's four classic plays is included (though it's my favourite), which makes this particular collection less essential.
And the letters (which are excepts from what is, I can only assume, a voluminous correspondence) do not really add to my experience of the stories, the real treasure.
But all and all, a good introduction to a man who might be considered the greatest short story author - or at least the most important - in history.