Leonard Euler biography sites:

http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Euler.htm 

"To those who ask what the infinitely small quantity in mathematics is, we answer that it is actually zero. Hence there are not so many mysteries hidden in this concept as they are usually believed to be. These supposed mysteries have rendered the calculus of the infinitely small quite suspect to many people. Those doubts that remain we shall thoroughly remove in the following pages. "

"Madam, I have come from a country where people are hanged if they talk." [In Berlin, excusing his taciturnity in conversation with the Queen Mother of Prussia, on his return from Russia]

1727 St Petersburg; Euler introduces the symbol e for the base of natural logarithms - not published until 1862.

1735 Euler introduces the notation f(x).

1748 Euler publishes Analysis Infinitorum (Analysis of the Infinite) . . defines a function, mathematical analysis is the study of functions. Bases calculus on the theory of elementary functions rather than on geometric curves, as previously. The famous formula ei = -1 appears for the first time.

1751 Euler publishes his theory of logarithms of complex numbers.

1752 Euler states his theorem V - E + F = 2 for polyhedra.

1765 Euler publishes Theory of the Motions of Rigid Bodies - the foundation of analytical mechanics.

1770 Euler publishes his textbook "Algebra."

1777 Euler introduces the symbol i to represent the square root of -1 in a manuscript which is not printed until 1794.

http://www-gap.dcs.st-and.ac.uk/~history/Chronology/1720_1740.html#1727

A Proof that e is Irrational
http://mathforum.org/isaac/problems/eproof.html

Euler's Seven Bridges of Konigsberg
http://mathforum.org/isaac/problems/bridges1.html

Euler's Formula
http://www.math.wichita.edu/history/topics/geometry.html#euler

Proofs of Euler's Formula
http://www.ics.uci.edu/~eppstein/junkyard/euler/

Platonic Solids and Euler
http://www.georgehart.com/virtual-polyhedra/platonic-info.html