Omar Al-Khayyam's famous book on algebra and equations is considered to be perhaps his most important contribution to mathematics - the cream of his work. Scholars of mathematics regard the book as an essential item in both their personal libraries and institutional collections. This book deals with the solution of quadratic and cubic equations. Al-Khayyam solved all possible cases of such equations by using geometrical approaches, sometimes involving conic sections such as parabolas and hyperbolas. The proofs presented are precise and very deep. The author made due acknowledgment and referral to the work and contributions of others who came before him. A modern reader may well be astonished by the high quality of the work, linguistically as well as mathematically. Historians of science, teachers of mathematics and mathematicians themselves will find the book both interesting and informative.