Many say the first computer is the "difference engine." The first of these devices was conceived in 1786 by J.H. Müller. It was never built.
Difference engines were forgotten and then rediscovered in 1822 by Englishman Charles Babbage..who is known as "the father of the Computer". This machine used the decimal numbers system and was powered by cranking a handle. The British government first financed the project but then later cut off support. Babbage went on to design his much more general analytical engine but later returned and produced an improved design (his "Difference Engine No. 2") between 1834 and 1869.
Others point out that this is the first ELECTRONIC computer. The earliest computer known is the Antikythera Machine, a mechanical device that computed the positions of the astrological signs on any given date, past or future. It was discovered in an ancient shipwreck in the Mediterranean Sea and dates to approximately 250 BC. The designer/builder is not known, but because of its similarity to other mechanical devices known to have been designed by Archimedes, it is probably his work.