Automatic computing has undergone drastic changes since the pioneering days of the early Fifties, one of the most obvious being that today the majority of computer programs are no longer written in machine code but in some programming language like FORTRAN or ALGOL. However, as desirable as the time-saving achieved in this way may be, still a high proportion of the preparatory work must be attributed to activities such as error estimates, stability investigations and the like, and for these no programming aid whatsoever can be of help. In this respect, ALGOL, as an internationally standardized notation which avoids computer-oriented concepts, provides another advantage, not often mentioned, but one which was already the guiding principle at the very beginning of the programming language venture: indeed, a correct ALGOL program is the abstractum of a computing process for which the necessary analyses have already been performed. It is the very purpose of this Handbook to establish such abstract formulations of certain computing processes. Therefore, numerical methods given in this Hand book in the form of ALGOL procedures may be put to immediate use wherever ALGOL is known and understood; in fact, application of such a method reduces to little more than calling the corresponding procedure.

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I Introduction.- § 1. The Concept of Automatic Programming.- § 2. Historical Remarks on Algorithmic Languages.- § 3. The Algol Conferences of 1958, 1960, 1962.- § 4. Algol Dialects and the IFIP Subset of Algol 60.- § 5. Preliminary Definition of Algol.- II Basic Concepts.- § 6. Auxiliary Conventions.- § 7. The Basic Symbols of Algol.- § 8. Values.- § 9. Quantities and their Names.- § 10. Numerical Constants.- § 11. Labels.- § 12. Strings.- § 13. Comments.- III Expressions.- § 14. Variables.- § 15. Function Designators.- § 16. Simple Arithmetic Expressions.- § 17. Relations.- § 18. Simple Boolean Expressions.- § 19. Conditional Expressions.- § 20. Subscript Expressions.- IV Statements.- § 21. Assignment Statements.- § 22. Sequences of Statements.- § 23. Labelled Statements.- § 24. The Dummy Statement.- § 25. Goto-Statements.- § 26. Procedure Statements I.- § 27. Compound Statements and Blocks.- § 28. The If-Statement.- § 29. The If-Else-Statement.- § 30. The For-Statement.- V Miscellaneous Applications.- § 31. Algebraic Problems.- § 32. Interpolation and Numerical Quadrature.- § 33. Numerical Integration of Differential Equations.- § 34. Least Square Problems.- §35. Computations Related to Continued Fractions.- § 36. Considerations Concerning Computer Limitations.- §37. Data Processing Applications.- VI Declarations.- § 38. Type Declarations.- § 39. Array Declarations.- § 40. Switch Declarations.- § 41. Procedure Declarations I.- §42. Semantics of Blocks.- §43. Entire Programs.- VII Procedures.- § 44. Procedure Declarations II.- §45. Procedure Statements II.- § 46. Function Procedures and their Use.- § 47. Code Procedures.- § 48. Parameter Procedures.- VIII Input and Output.- § 49. The Standard I/O-Procedures of Algol.- §50. Applications of Procedures insymbol, outsymbol.- §51. Use of inarray, outarray for Auxiliary Storage.- Appendix A.- § 52. The Jensen Device.- 52.1. The full name-concept.- 52.2. The Jensen device.- 52.3. Bound variables.- § 53. Conclusion.- 53.1. Church's lambda notation.- 53.2. The lambda notation for arrays.- 53.3. Syntax of the proposed extension.- 53.4. Semantics of the proposed extension.- 53.5. Applications of the proposed extension.- Appendix B. The IFIP-Reports on Algol.- References.