'Transactional Analysis is a theory of personality and a systematic psychotherapy for personal growth and personal change'.
It is also a theory of child development and communication, a way of looking at language and behaviours to understand (amongst other things) when our thoughts and actions are being affected by past influences. Originally developed by Eric Berne in the early 1960's, it has gained over the years from later research and experience - although the concept of Parent, Adult and Child ego states remains central.
Based on an equal relationship of 'I'm ok, you're ok' between therapist and client, it is rooted in experience and seeks to be both rational and accessible - using plain English and encouraging clients to be fully involved in the process. It is contractual, with clear boundaries and targets.
The link below gives further details and it is possible to go on 'TA101' weekends that explore the principles and background.