Adding Machine
Pascal

Aeroplane
Wright brothers

Air Brake
George Westinghouse

Air Pump
Otto von Guericke

Airship (rigid)
G. Ferdinand Von Zeppelin

Aniline Dyes
Hoffman

Antiseptic Surgery
Lord Joseph Lister

Arc Lamp
C. F. Brush

Archimedean Screw
Archimedies

Atom
Neils Bohr

Atom Bomb
J Robert Oppenheimer (Not discoverer but is often known as the father of atomic bomb)

Atomic Number
Mosley

Atomic Physics
Enrico Fermi

Atomic Structure
Bohr and Rutherford

Atomic Theory
Dalton

Automatic gearbox
Hermann Fottinger

Automobile
Daimler

Automobiles using gasoline
Karl Benz

Avogadro’s Hypothesis
Avogadro