2007 is the three hundredth anniversary of the birth of Leonhard Euler. As a result there is likely to be a resurgence of interest in him and of course his work. His Elements of Algebra is one of the first books to set out elementary algebra in the modern form we would recognize today. However, it is sufficiently different from most modern approaches to the subject to be interesting for contemporary readers. Indeed, the choices made for setting out the curriculum, and the details of the techniques Euler employs, may surprise even expert readers. It is also the only mathematical work of Euler which is genuinely accessible to all. The work opens with a discussion of the nature of numbers and the signs + and -, before systematically developing algebra to a point at which polynomial equations of the fourth degree can be solved, first by an exact formula and then approximately. Euler's style is unhurried, and yet rarely seems long winded.