Table of contents : To my readers. On our inability to do much. On the reliability of mechanisms. On our mental aids. An example of a correctness proof. Cn the validity of proofs versus the validity of implementations. On understanding programs. On comparing programs. A first example of step-wise program composition. On program families. On trading storage space for computation speed. On a program model. A second example of step-wise program composition. On what we have achieved. On grouping and sequencing.