A gas turbine engine comprising: a main compressor section having a high pressure compressor with a downstream discharge, and more upstream locations; a turbine section having a high pressure turbine; an accessory gearbox; a tower shaft configured to be driven by the main compressor section, the tower shaft configured to drive the accessory gearbox; and an intercooling system comprising: a shaft; a cooling compressor mounted to the accessory gearbox; and a heat exchanger for cooling air drawn from a portion of the main compressor section at a first temperature and pressure to a second temperature cooler than the first temperature, the cooling compressor configured to compress air communicated from the heat exchanger to a second pressure greater than the first pressure and configured to communicate the compressed air to a portion of the turbine section, and the accessory gearbox configured to drive at least one component (112, 114, 116) different than cooling compressor and includes pads defining mounting locations for accessory components (112, 114, 116), and the cooling compressor is mounted to one of the pads of the accessory gearbox, the accessory gear box configured to drive the cooling compressor; characterised in that: the intercooling system further comprises a tap configured to tap air from at least one of the more upstream locations in the main compressor section and pass the tapped air through the heat exchanger and then to the cooling compressor; and the cooling compressor includes a centrifugal compressor impeller that is turned by the shaft, wherein the shaft supports a first gear that is driven by a second gear mounted to the tower shaft. a main compressor section having a high pressure compressor with a downstream discharge, and more upstream locations; a turbine section having a high pressure turbine; an accessory gearbox; a tower shaft configured to be driven by the main compressor section, the tower shaft configured to drive the accessory gearbox; and an intercooling system comprising: a shaft; a cooling compressor mounted to the accessory gearbox; and a heat exchanger for cooling air drawn from a portion of the main compressor section at a first temperature and pressure to a second temperature cooler than the first temperature, the cooling compressor configured to compress air communicated from the heat exchanger to a second pressure greater than the first pressure and configured to communicate the compressed air to a portion of the turbine section, and the accessory gearbox configured to drive at least one component (112, 114, 116) different than cooling compressor and includes pads defining mounting locations for accessory components (112, 114, 116), and the cooling compressor is mounted to one of the pads of the accessory gearbox, the accessory gear box configured to drive the cooling compressor; a shaft; a cooling compressor mounted to the accessory gearbox; and a heat exchanger for cooling air drawn from a portion of the main compressor section at a first temperature and pressure to a second temperature cooler than the first temperature, the cooling compressor configured to compress air communicated from the heat exchanger to a second pressure greater than the first pressure and configured to communicate the compressed air to a portion of the turbine section, and the accessory gearbox configured to drive at least one component (112, 114, 116) different than cooling compressor and includes pads defining mounting locations for accessory components (112, 114, 116), and the cooling compressor is mounted to one of the pads of the accessory gearbox, the accessory gear box configured to drive the cooling compressor; the intercooling system further comprises a tap configured to tap air from at least one of the more upstream locations in the main compressor section and pass the tapped air through the heat exchanger and then to the cooling compressor; and the cooling compressor includes a centrifugal compressor impeller that is turned by the shaft, wherein the shaft supports a first gear that is driven by a second gear mounted to the tower shaft.