A core analytical tool; contradictions are the inherently opposed logical extensions or compositions of any given state of affairs. Contradiction is what drives change as two or more incompatible propositions hold sway for varying periods of time and gradually resolve.
Contradictions may be antagonistic or non-antagonistic and may also be primary, secondary, or tertiary. They may also be internal or external.
Antagonistic contradictions are those contradictions which cannot resolve without systemic change. These are essentially contradictory.
Non-antagonistic contradictions are only in contradiction due to one or more temporary constellations of material conditions and may fall out of contradiction. These are accidentally contradictory.
Primary contradictions are the driving contradictions from which other pairs and clusters of contradictions arise during any given period. Without the resolution of primary contradictions, the underlying problems are not solved.
Whether a contradiction is internal or external is a matter of perspective. Internal contradictions are contradictions between elements or conditions that are within a single analyzed system or unit (internal contradictions of capitalism, say) and external contradictions are those which arise from outside that unit (contradiction between an element of capitalism and, for example, the environment). However, when performing material analysis, it is always possible to shift frame of reference and thus re-categorize contradictions are either internal or external.