Marcel Brissaud, during the seventies, has been the first to observe the

interest of developing mathematical concepts adapted to humanities.

Pretopology theory relies on the statement that the axiomatic of mathematical

topology is too strong to model the phenomena of social sciences. This

axiomatic has to be reconsidered to give birth to a theory that is adapted to

data issued from these fields of expertise, better than trying to force data to

fit to an existing and inadequate theory.

This book is the first English revised version of a first book, published in

French, which is planned to be the first of a series dedicated to the whole set

of results obtained in Pretopology: continuity, connectedness, associated

metric...

Many applications of Pretopology were conducted in various fields: economy

with the structural analysis of a economy, game theory with the study

of the dynamics of coalitions in cooperative games, sociology with analysis

of social networks, data analysis with the construction of clustering algorithms,

pattern recognition with digital image analysis as in mathematical

morphology, etc.

Purely mathematical work in Pretopology has enabled the building of processing

algorithms that have been put in a software library, Pretopolib,

allowing researchers to implement a pretopological approach in their

work.

We wish the reader of this book the pleasure of exploring the basics of

Pretopology and we hope that he will find the materials for his own work

and we give him a rendez-vous for the next books on the subject.