  In this paper we are concerned with the structure of tame symmetric algebras
of period four (TSP4 algebras, for short). We will mostly focus on the case
when the Gabriel quiver of $A$ is biserial, i.e. there are at most two arrows
ending and at most two arrows starting at each vertex, but some of the results
can be easily extended to the general case. This serves as a basis for upcoming
series of articles devoted to solve the problem of classification of all TSP4
algebras with biserial Gabriel quiver. We present a range of properties (with
relatively short proofs) which must hold for the Gabriel quiver of a tame
symmetric algebra of period four. Amongst others we show that triangles (and
squares) appear naturally in the Gabriel quivers of such algebras, such as for
weighted surface algebras [6, 8, 9].
