Metric measure spaces with Ricci bounds from below

In this survey we introduce new results on metric measure spaces with Ricci curvature bounded below, so-called <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper R normal upper C normal upper D"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">R</mml:mi> <mml:mi mathvariant="normal">C</mml:mi> <mml:mi mathvariant="normal">D</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathrm {RCD}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> spaces, including stability results of several energies with respect to measured Gromov-Hausdorff convergence, Weyl’s law, and a characterization of noncollapsed RCD spaces.