to say anything new per se, but rather to present definitions, facts, and proofs most of which are well known, at least as folklore, in a simple and accessible format.

Historical remarks
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The importance of the Self-Linking Integral is that it is the most simple and basic example of presentation of a Vassiliev invariant as a configuration space integral. Moreover, as the work of Bott and Taubes [@BT] (see also [@AF]) shows, this integral plays a basic role as a correction term for anomalies in the definition of more general finite-type “self-linking invariants”. In this regard, this invariant constitutes a basic ingredient in the understanding of the Chern-Simons invariants of knot theory.

The first effective ‘renormalization’ of the Gauss integral by adding a correction term was carried out by Calugareanu [@Cal], and later by Pohl [@Poh] in the case of a closed space curve with nowhere vanishing torsion.

Who the first person was to extend the invariant to curves that may have a non-vanishing torsion I do not know. The ‘holonomy’ construction (the second method above) appears the more common, and is used for instance by Polyakov [@Pol] (see also Tze [@Tze]), by Bott and Taubes [@BT] and by 