  In this paper, we consider Lorentz--Karamata spaces with slowly varying
functions and provide a comprehensive study of their properties.
  We consider Lorentz--Karamata functionals over an arbitrary sigma-finite
measure space equipped with a non-atomic measure and the corresponding
Lorentz--Karamata spaces. We characterise non-triviality of said spaces, then
study when they are equivalent to a Banach function space and obtain a complete
characterisation. We compute the fundamental function of said spaces and
describe the corresponding endpoint spaces. We further provide a complete
characterisation of when the Lorentz--Karamata spaces defined using
non-increasing rearrangement are equivalent to those defined using maximal
function. We provide a complete description of the associate spaces of
Lorentz--Karamata spaces. We also treat other topics like embeddings, absolute
continuity of the (quasi)norm, and Boyd indices.
