Convergent Series is the second Larry Niven anthology I've read over the past month and I enjoyed it far more than Tales of Known Space.
In terms of quantity, there were more stories in Convergent Series (twenty-one to be exact) with several only two or three pages long. Five of the stories are from his popular Draco's Tavern series.
Some of my favorites from this anthology include:
"Bordered in Black" - Two astronauts scouting an alien world detect a strange black border along the shoreline of the largest ocean. Theorizing that it's dead algae washed ashore, they land to investigate--only to discover just how horribly wrong they were!
"The Meddler" - Targeted by a wealthy crime boss named Sinc, private eye Bruce Cheseborough decides to confront the kingpin on his own turf. Accompanied by a shapeshifting alien anthropologist, whose function is merely to observe, Cheseborough confronts Sinc in his mansion, only to discover a surprising connection to the metamorph.
"Dry Run" - As practice for murdering his ex-wife and dumping her body in the ocean, a man kills her dog--then ends up in a car accident on his way to dispose of the carcass lying in his trunk.
"Convergent Series" - An anthropology student takes an interest in dark magic and accidentally conjures a demon inside a pentagram drawn on the basement floor. Now, how to outwit the beast and send him back from whence he came...
"Singularities Make Me Nervous" - After exploring the space near a blackhole, astronaut George Cox returns to his apartment to confront...himself! This is no surprise to him, as Cox has traveled back in time in before in the same repeating loop. His younger self, however, is unsure how to handle the situation--until the pair conspire a scam that could make them millions.
"Mistake" - After dosing on sedatives to help him survive a lenthy spaceflight, Commander Elroy Barnes is confronted by a telepathic alien named Kthitslmup, who attempts to probe the commander's mind with little success thanks to the drugs. The alien then resorts to verbal questioning. In order to answer, Barnes must take another pill to clear his mind, which holds an interesting consequence for Kthitslmup.
"Night on Mispec Moor" - A contract warrior in a corporate-sponsored battle abandons the fight and takes refuge atop a large rock formation--until nightfall when the dead soldiers rise from the mists of the battlefield to stalk the living...
"Wrong Way Street" - A team of scientsts is sent to the moon to study an ancient, deserted alien base and spaceship. Aboard the ship, one particular machine perplexes Mike Capoferr. He has his theories, which are proven correct when he finally learns how to activate it...regrettably.