This book contains the lectures delivered at the Fourth Paris Cosmology Colloquium held at the Observatoire de Paris from June 4 - 9, 1997. This Colloquium ‘Phase Transitions in Cosmology’ is the first event of a EUROCONFERENCE series (‘Accompanying Measures’), with the support of the training and Mobility Programme of the Commision of the European Communities.The purpose of the Paris Cosmology Colloquia is to cover selected topics of high current interest in the interplay between cosmology and fundamental physics and to allow easy and fruitful interaction and communication between researchers in these areas. The main aim is to put in contact fundamental theoretical physics (including string theory) with real physical problems that arise in the study of the universe. The Paris Cosmology Colloquia are informal meetings which bring together physicists, astrophysicists and astronomers. Topics covered in this Fourth Paris Cosmology Colloquium included: cosmic microwave background, phase transitions in cosmology and evolution out of the equilibrium quantum fields, the value of the Hubble constant, fundamental strings in primordial cosmology, as well as other subjects of high current interest such as scaling laws in the interstellar medium and in the large scale structure, gravitational lensing and dark matter.