Two 29-year-old men were assaulted by three men with machetes near The Vital Spark pub in Govan Road at 7pm on Sunday. One was injured seriously on the hand while the other man was cut on the head.
About an hour later a 24-year-old man was found with stab wounds to his neck and thigh in a house in Balbeg Street in the south-west area of the city.
Later that evening at around 10pm, a 21-year-old was attacked with a bottle and received a cut to the head at Gleddoch/Penilee Park in Glasgow.
None of the men's injuries are life-threatening and none of the incidents are thought to be connected.
Detective Inspector Alan McAlpine, of Glasgow CID, said: "I wish to emphasise that attacks of this type are very rare."