This book offers a comprehensive introduction to the theory of
linear and nonlinear Volterra integral equations (VIEs), ranging
from Volterra's fundamental contributions and the resulting
classical theory to more recent developments that include Volterra
functional integral equations with various kinds of delays, VIEs
with highly oscillatory kernels, and VIEs with non-compact
operators. It will act as a 'stepping stone' to the literature on
the advanced theory of VIEs, bringing the reader to the current
state of the art in the theory. Each chapter contains a large
number of exercises, extending from routine problems illustrating
or complementing the theory to challenging open research problems.
The increasingly important role of VIEs in the mathematical
modelling of phenomena where memory effects play a key role is
illustrated with some 30 concrete examples, and the notes at the
end of each chapter feature complementary references as a guide to
further reading.
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