  Topological solitons are knots in continuous physical fields classified by
non-zero Hopf index values. Despite arising in theories that span many branches
of physics, from elementary particles to condensed matter and cosmology, they
remain experimentally elusive and poorly understood. We introduce a method of
experimental and numerical analysis of such localized structures in liquid
crystals that, similar to the mathematical Hopf maps, relates all points of the
medium's order parameter space to their closed-loop preimages within the
three-dimensional solitons. We uncover a surprisingly large diversity of
naturally occurring and laser-generated topologically nontrivial solitons with
differently knotted nematic fields, which previously have not been realized in
theories and experiments alike. We discuss the implications of the liquid
crystal's non-polar nature on the knot soliton topology and how the medium's
chirality, confinement and elastic anisotropy help to overcome the constrains
of the Hobart-Derrick theorem, yielding static three-dimensional solitons
without or with additional defects. Our findings will establish chiral nematics
as a model system for experimental exploration of topological solitons and may
impinge on understanding of such nonsingular field configurations in other
branches of physics, as well as may lead to technological applications
