  In the paper we describe the class of principal quandles and show that
connected quandles can be decomposed as a disjoint union of principal quandles.
We also prove that simple affine quandles are finite and they can be
characterized among finite simple quandles by several different equivalent
properties, as for instance being doubly homogeneous (i.e. having a doubly
transitive automorphism group). A complete description of finite
doubly-homogeneous quandles is provided extending the result of \cite{V} and
solving \cite[Problem 6.7]{2trans}. We also provide a classification of
connected cyclic quandles with several fixed points independently from
\cite{CQ}.
