this book introduces value distribution theory over non-archimedean fields, starting with a survey of two nevanlinna-type main theorems and defect relations for meromorphic functions and holomorphic curves. secondly, it gives applications of the above theory to, e.g., abc-conjecture, warings problem, uniqueness theorems for meromorphic functions, and malmquist-type theorems for differential equations over non-archimedean fields. next, iteration theory of rational and entire functions over non-archimedean fields and schmidts subspace theorems are studied. finally, the book suggests some new problems for further research. audience: this work will be of interest to graduate students working in complex or diophantine approximation as well as to researchers involved in the fields of analysis, complex function theory of one or several variables, and analytic spaces.