This i s a substantiall y revise d se t o f lectur e note s originall y publishe d i n 200 5
at IMPA , Brazil , unde r a slightly differen t title : "Dynamics of infinite-dimensional
groups and Ramsey-type phenomena".
The boo k ha s bee n restructure d an d expande d an d i n th e presen t for m con -
tains abou t a quarte r mor e material . Also , I hav e mad e a considerabl e numbe r o f
corrections an d updates .
I a m gratefu l t o Serge i Gelfan d an d t o Vital i Milman , wh o hav e mad e thi s
publication possible , a s wel l a s t o Arlen e O'Sea n an d t o Christin e Thivierg e fo r
their editoria l help .
Vladimir Pesto v
Gloucester, Ontario , Septembe r 25 , 2006
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