Short answers, pulled from the story.
Classical mechanics is a theory that describes the effect of forces on the motion of macroscopic objects and bulk matter, without considering quantum effects and often without relativistic effects. It is used to describe objects such as projectiles, machinery, spacecraft, planets, stars, galaxies, deformable solids, fluids, and macromolecules.
Classical mechanics was traditionally divided into statics, kinematics, and dynamics. Statics analyzes force and torque on a system in equilibrium, kinematics describes the motion of bodies without considering the forces that cause it, and dynamics considers the forces that explain that motion.
Isaac Newton laid the foundations of classical mechanics with three laws of motion and his law of universal gravitation, set out in his Philosophiae Naturalis Principia Mathematica. Energy-based methods were later developed by Euler, Joseph-Louis Lagrange, and William Rowan Hamilton, and earlier contributors included Johannes Kepler, Galileo, and Christiaan Huygens.
Newtonian mechanics emphasizes force as a vector quantity, while Lagrangian and Hamiltonian mechanics use scalar properties such as kinetic and potential energy. Lagrangian mechanics uses generalized coordinates and velocities, Hamiltonian mechanics uses coordinates and momenta, and the two are linked by a Legendre transformation so they contain the same information.
Classical mechanics provides accurate results for objects that are not extremely massive and move at speeds far below the speed of light. For objects about the size of an atom's diameter it gives way to quantum mechanics, for speeds approaching light it requires special relativity, and for extremely massive objects general relativity becomes applicable.
Joseph-Louis Lagrange presented his work to the Turin Academy of Science in 1760, culminating in his 1788 grand opus Mecanique analytique. William Rowan Hamilton reformulated Lagrangian mechanics in 1833 by replacing generalized velocities with generalized momenta.