Course to be flown

Under IFR in controlled airspace, you don't get to wander — § 91.181 says you must fly a defined course unless ATC authorizes otherwise:

• on an ATS route (airway): along the centerline of that airway; and
• on any other route: along the direct course between the navaids or fixes that define the route.

The point is predictability: ATC separates IFR traffic on the assumption you're tracking the airway centerline or the direct course you were cleared on, not drifting off it.

The rule preserves common-sense flexibility, though. It doesn't prohibit maneuvering to pass well clear of other traffic, and it lets you maneuver in VFR conditions to clear your intended flight path before and during a climb or descent. So you can deviate enough to keep yourself safe — but the baseline expectation is that you stay on the cleared centerline/course.

Summary: Under IFR in controlled airspace you must fly the airway centerline (or, off-airway, the direct course between the defining fixes) unless ATC authorizes otherwise — with allowances to maneuver clear of traffic and to clear your flight path in VFR conditions.