WordNet sense 1 (break down into components or essential features):

analyse

WordNet sense 2 (consider in detail and subject to an analysis in order to discover essential features or meaning):

canvas, canvass, examine, study

WordNet sense 3 (make a mathematical, chemical, or grammatical analysis of; break down into components or essential features):

dissect, break down, take apart

WordNet sense 4 (subject to psychoanalytic treatment):

psychoanalyze, psychoanalyse