Re-opening of assessment permits reassessment where tax base escaped assessment, subject to recorded reasons and time limits and procedural safeguards. The provision authorises reopening an assessment where the Assessing Officer, for reasons recorded in writing, believes tax bases have escaped assessment; reopening is effected by notice requiring a return of tax bases, applies in specific circumstances including non-filing, understatement, under-assessment, and search or requisition material, is subject to seven year and supervisory time limits, allows reassessment at appropriate tax rates, extends to other persons affected by seized or requisitioned material, and permits dropping proceedings where the original assessment already reflects the correct liability.