List of Figures

	Figure 1: The Feynman propagator and three- and four-point vertices in Einstein gravity.
	Figure 2: Sample gravity tree-level Feynman diagrams. The lines represent any particles in a gravity theory.
	Figure 3: Sample loop-level Feynman diagrams. Each additional loop represents an extra power of Planck’s constant.
	Figure 4: An example of a five-loop diagram.
	Figure 5: String theory suggests that the three-graviton vertex can be expressed in terms of products of three-gluon vertices.
	Figure 6: The color-ordered gauge theory Feynman rules for obtaining tree-level scattering amplitudes for gravity coupled to matter, via the KLT equations. The Greek indices are space-time ones and the Latin ones are group theory ones. The curly lines are vectors, dotted ones scalars, and the solid ones fermions.
	Figure 7: The three color-ordered Feynman diagrams contributing to the QCD partial amplitude in Eq. (15 ).
	Figure 8: As two momenta become collinear a gravity amplitude develops a phase singularity that can be detected by rotating the two momenta around the axis formed by their sum.
	Figure 9: The two-particle cut at one loop in the channel carrying momentum $k1 + k2$ . The blobs represent tree amplitudes.
	Figure 10: Two examples of generalized cuts. Double two-particle cuts of a two-loop amplitude are shown. This separates the amplitude into a product of three tree amplitudes, integrated over loop momenta. The dashed lines represent the cuts.
	Figure 11: The one-loop box integral. Each internal line in the box corresponds to one of the four Feynman propagators in Eq. (51 ).
	Figure 12: The planar and non-planar scalar integrals, appearing in the two-loop $N = 8$ amplitudes. Each internal line represents a scalar propagator.
	Figure 13: Starting from an $l$ -loop planar diagram representing an integral function, an extra line may be added to the inside using this rule. The two lines on the left represent two lines in some $l$ -loop diagram.