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This manual describes the operations available with the Advanced Continuous Simulation Language, ACSL (pronounced 'axle'). This language is designed for modelling and evaluating the performance of continuous systems described by time dependent, nonlinear differential equations. In the development of the simulation system, emphasis has been placed on the ability to run and evaluate the model on-line. Provision has been made to overcome the usual problem of high data volume; i.e. monitoring information can be directed to the terminal, high volume output to a local line printer. In becoming familiar with this manual, it is recommended that the reader look through Chapters 1, 2 and 3 and then turn to the example programs given in Appendix A, making reference to the operators (Chapter 4) and runtime commands (Chapter 5) as necessary. Chapter 4 and 5 are not designed for direct reading because of the alphabetic organization of the material. Before running a simulation, be sure to study Chapter 7 on program debugging. The fourth edition includes updated information on the features and functions available (in the description in Chapter 4 and 5 and Appendix C, and the summary tables in Appendix D). In addition, Chapters 4 and 5 begin each section with specifications on the form for each call, command, or subcommand being described in the section. The description of the ANALYZ command (Section 5.2) has been updated and expanded. A new section has been added on the SCHEDULE event-finder function (Section 4.97), as well as an example in Appendix A which illustrates use of SCHEDULE (Section A13, Block on a Rough Surface). Chapter 6 on Macro Language now includes a section on matrix operations (Section 6.4.4) with code for several useful macros.