The Concorde wasn't the first super sonic aircraft. The honors belong to the Tupolev TU-144, the USSR's only super sonic transport. Its one of two super sonic transports that was ever built for commercial use other than the Concorde. It was designed in 1962 and saw its first prototype flying on New Year's eve of 1968 outside Moscow. This was just two months before Concorde took flight.
The Tupolev looks a lot like the Concorde, but the two planes differ in technical aspects. The Concorde had better range, braking and engine control, but the Tupolev was better in aerodynamics. Its wings included two small retractable canard surfaces for generating low speed lift that the Concorde lacked. It was also less stable in flight, especially at supersonic speeds.
Because of that, its very first production model crashed at the Paris Auto Show, killing six crewmen and eight people on the ground. The cause of the crash remains undertermined, the French and Russian governments still blame each other for the plane's crash. The Russians think its a mysterious French Mirage fighter jet appeared to be tailing the TU-144 before it went down. The French accused the Soviet flight crew of trying to bank the plane too hard.
Overall, it was a dismal failure. It proved unreliable in commercial flight, and the first 16 TU-144s suffered more than 226 failures, a third of them in the air. It spanned from things like cabin noise to cabin depressurization. Due to all these failures, the plane was cancelled in 1983. [TU-144 Wiki - TU144 - Tupolev 144 - Pilot Friends]