This is not a full description of SVG but it should give the reader some idea of the parts of SVG that are relevant to SVG declarative animations.
SVG is a simple 2D drawing language aimed at the web with one great advantage: it does have facilities for declarative animation albeit with a need to be quite precise in how the animation is described.
The declarative animation facilities were jointly defined with the group working on the SMIL multimedia recommendation. In consequence, some people refer to the declarative animations facilities as SMIL animation which is incorrect for two reasons. Firstly, not all of the SVG animation facilities are defined in SMIL and secondly, they are a formal part of the SVG standard.
An early comprehensive primer can be found on the W3C web site at http://www.w3.org/Graphics/SVG/IG/resources/svgprimer.html.
A more recent primer in SVG is Ivan Herman's (2004) at https://www.w3.org/Consortium/Offices/Presentations/SVG/
The new version of SVG currently being worked on can be found at https://svgwg.org/svg-next/Overview.html.