Mathematical Analysis & its Applications is the four-year programme associated with the Maxwell Institute Graduate School in Analysis and its Applications (MIGSAA), a Centre for Doctoral Training that provides high quality instruction in analysis and the applications of analysis to a wide range of areas. MIGSAA has been made possible by a grant from the UK's Engineering and Physical Sciences Research Council and the Scottish Funding Council. The programme is delivered in collaboration with Heriot-Watt University. PhD study in MIGSAA may be undertaken with over 40 supervisors and on topics ranging from pure analysis to applied mathematics relevant for scientific, engineering, environmental or social challenges. As opposed to a standard PhD, MIGSAA students are admitted to the programme (rather than with a specific supervisor), and take PhD training courses and projects over their first year, which help shape their perspective, leading to a match with a supervisor in the second half of Year 1. The research project directed by the supervisor is still the centrepiece of the PhD, but this is augmented by an on-going training programme in Years 2-4 of the student's studies.