Alien Emergencies contains 3 of James White Sector General novels.
The first is Ambulance Ship is which the protagonist, Dr. Conway, is put in charge of the ambulance ship Rhabwar, whose mission is to respond to emergency beacons that are likely to by first contact situations. It is clearly a series of stories with a bit of connecting material. Still the stories are interesting and Mr. White has a real talent for imagining aliens who are very alien. It is a good book.
The second novel is Sector General and it is a bit of a let down. Like the first it was clearly a series of stories. By this time I found the stories were getting to be formulaic and I wished for a bit more variety. It is still interesting, but not dazzling.
The third novel is Star Healer and I think it was written as a novel. Certainly it feels that way. This one is really excellent. The characters are vivid and the medical problems absorbing and alien. This book is outstanding.
Overall if you are interested SF from a different angle, I think you will enjoy all of the books in this edition, and, indeed, all of James White's Sector General stories. Step into Sector General and be amazed.
Good stories though they tend to get a bit long winded at times.