It could be argued that the abacus is the first device for ‘computing, invented in Chine between 2600 BC and 300 BC- it was used for tabulating numbers and

The "difference engine" conceived in 1786 by J.H. Müllerr is arguably the first of device like a computer.  Müllerr’s  devices was never built, and the plans were discovered by Charles Babbage in 1822, who is credited as creating the first computer.    Babbage’s device used a crank handle and a number system, sort of like a massive calculator, and was part funded by the British Government.  It was later improved as a general analytical engine but later returned and produced an improved design (his "Difference Engine No. 2") between 1834 and 1869.

If you mean Electronic Computer that would be recognisable by modern standards then Alan Turing from Cambridge UK, in the employ of the British Governent created a machine to crack the enigma codes named Colossus, which was the worlds first digital, electronic computing device.  Much of Turing’s work was top secret until recently. 

Paper tapes, used as information storage for control purposes were first employed in the 1720s by Basile Bouchon and Jean-Baptiste Falcon to control looms. By changing tapes, one could quickly reprogram the loom to weave different patterns. Joseph Jacquard more fully automated loom control with punched cards in 1801. These cards were used by Babbage in his computing machines to order the sequence of calculations.

Charles Babbage (1791-1871) is considered by many to be the inventor of the computer. He designed two machines, a "difference engine" and an "analytical engine" which used algorithms to calculate complex equations algorithmically.

The first programmer was Ada Byron, Lady Lovelace (1815-1852), daughter of the famous Romantic poet Lord Byron. In 1843, Ada developed a plan for how his machines could calculate Bernoulli numbers; this plan is normally credited as the first computer program.

More complex calculating and tabulating machines evolved in the early twentieth century, until the first general purpose electronic computer, the ENIAC (Electronic Numerical Integrator and Computer), was developed in 1941-1945.

Soon after the invention of the computer was the discovery by Grace Hopper of the first computer bug, a moth trapped in a relay of the Harvard University Mark II Aiken Relay Calculator on 9 September, 1945.