An anaesthetic breathing system is a means of transferring the breathing gas mixture from the anaesthetic machine common gas outlet to the patient. It is also the means of transferring the exhaled gas from the patient to the outside world, usually via a scavenging system. Alternatively, after the carbon dioxide is absorbed from the exhaled gas, the unused fresh gas components of the exhaled gas are recirculated back to the patient. In general, a breathing system consists of a fresh gas limb, an inspiratory and expiratory limb, an expiratory valve, a reservoir bag and it may also consist of one or more unidirectional valves and a CO2 absorber. The simpler devices have fewer components and usually involve some rebreathing of expiratory gas, depending on the level of fresh gas flow. The ability to minimise rebreathing at as economical a fresh gas flow as possible is a measure of the breathing system’s efficiency. Depending on the precise design of the breathing system, such efficiency will vary depending on whether the patient is breathing spontaneously or is undergoing controlled artificial ventilation (see Chapter 26). The more complex systems ensure minimum rebreathing by the use of unidirectional valves and CO2 absorption systems; in this way, the additional complexity allows more economical use of fresh gas and volatile agent. The systems that use higher fresh gas flows (FGF) and involve some rebreathing were classified in 1954 by Professor Mapleson, according to their behaviour in terms of the FGF requirement to prevent CO2 rebreathing [Mapleson 1954]. At the time and for three decades beyond, they were the most popular breathing systems in UK anaesthetic practice. The Mapleson Classification of rebreathing systems is shown in Figure 25.1. Their design lends their structure and function to mathematical analysis [Dorrington 1989]. The Magill breathing system was invented by Sir Ivan Whiteside Magill in the early twentieth century. As shown in Figure 25.1A and Figure 25.2, the system is characterised by having the expiratory valve close to the patient and the fresh gas inflow at a distance from the patient, but close to the reservoir bag. Because of this particular configuration, the system is very economical in spontaneous breathing.