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Multiply lensed sources experience a relative time delay in the arrival ofphotons. This effect can be used to measure absolute distances and the Hubbleconstant ($H_0$) and is known as time-delay cosmography. The methodology isindependent of the local distance ladder and early-universe physics andprovides a precise and competitive measurement of $H_0$. With upcomingobservatories, time-delay cosmography can provide a 1% precision measurement of$H_0$ and can decisively shed light on the current reported 'Hubble tension'.This paper presents the theoretical background and the current techniquesapplied for time-delay cosmographic studies and the measurement of the Hubbleconstant. The paper describes the challenges and systematics in the differentcomponents of the analysis and strategies to mitigate them. The currentmeasurements are discussed in context and the opportunities with theanticipated data sets in the future are laid out.

Time-Delay Cosmography: Measuring the Hubble Constant and other cosmological parameters with strong gravitational lensing