Book intended for university students (undergraduates) and all those who wish to know more about the astonishing numbers that are e, π and i. The book is structured around solved exercises or problems. It details the study of the e, π and i numbers, so familiar to science students. Familiar ? ... not so sure ... How did we come to create the exponential and logarithm functions ? How do we calculate the values of e and π ? Thanks to which formulas ? And where do these formulas come from ? When and how were they discovered ? And by whom ? In the midst of the Italian renaissance, some mathematicians, seeking to solve equations of the type x3 + px + q = 0 bring to light, dumbfounded, an imaginary number that came out of nowhere but essential to their calculations. They do not yet realize that they have just discovered complex numbers ! How did they do it ? Can π and e be written in fractional form ? These questions and their answers are dealt with throughout the book in the form of corrected exercises calling on the basic mathematical knowledge acquired in classroom. Euler's method for the calculation of e; Archimedes' method, of Snellius, of Machin, of Brent-Salamin, BBP are reviewed for the calculation of π. Elementary algorithms for computer programming complete the study. The last exercise of the book concerns the demonstration of the relation: eix = cosx + i sinx to highlight Euler's formula: eiπ + 1 = 0 we have to face the facts: π, e and i are linked together ! Plan of the book : 1 - Reminders about sets of numbers sets of numbers classification other type of classification - transcendence 2 - Power and exponential functions power functions (solved problem) exponential and logarithm functions (solved problem) 3 - e, the Euler number search for e by two different sequences (solved problem) e is irrational (solved problem) 4 - π , the number of Archimedes knowledge of the circle - definition of π and interest calculation of π by Archimedes' method (solved problem) calculation of π by Snellius method (solved problem) calculation of π by Machin's method (solved problem) calculation of π by the Brent-Salamin method (solved problem) calculation of π by the method of Bailey-Borwein-Plouffe (solved problem) π is irrational (solved problem) 5 - i and complex numbers discovery of i when solving x3 + px + q = 0 (solved problem) history of complex numbers : algebraic form trigonometric form (solved exercise) exponential form (solved exercise) e , π , i are related to each other by Euler's formula : eiπ + 1 = 0