  A new mathematical object called a skand is introduced, which turns out in
general to be a non-well-founded set. Skands of finite lengths are ordinary
well-founded sets, and skands of very long length (like the hyper-skand of all
ordinals) are hyper-classes.
  Self-similar skands are also considered, and they clarify the reflexivity of
sets, i.e., the meaning of the relation X is a member of X; in particular,
self-similar skands considered as non-well-founded sets are always reflexive,
but not vice versa. The existence of self-similar skands shows at once that
Russell's well-known paradox is not a paradox at all. The inconsistency of
Russell's "set" R, which is the collection of all sets that are not members of
themselves, is proved here not with the help of Russell's paradox (as it is
traditionally given, which is incorrect), but via a simple method of the
maximality (universality) of R which goes back to Cantor and can be also
applied to other set-theoretical paradoxes.
  Generalized skands are also defined and a new look at the generalized
skand-class of all ordinals is demonstrated. In particular, the last (class)
ordinal called the eschaton is defined.
  The next application of skand theory is a description of all epsilon-numbers
in the sense of Cantor. Another application is a generalized theory of
one-dimensional continua of arbitrary powers and the construction of
generalized real numbers as a non-Archimedean straight line of arbitrary power,
and the introduction of the absolute continuum and the absolute straight line
as the hyper-classes nearest to the class of sets.
