High Precision Optical Spectroscopy and Quantum State Selected Photodissociation of Ultracold 88Sr2 Molecules in an Optical Lattice : Springer : 9783319687346 : 3319687344 : 28 Nov 2017 : This thesis unites the fields of optical atomic clocks and ultracold molecular science, laying the foundation for optical molecular measurements of unprecedented precision. Building upon optical manipulation techniques developed by the atomic clock community, this work delves into attaining surgical control of molecular quantum states. The thesis develops two experimental observables that one can measure with optical-lattice-trapped ultracold molecules: extremely narrow optical spectra, and angular distributions of photofragments that are ejected when the diatomic molecules are dissociated by laser light pulses. The former allows molecular spectroscopy approaching the level of atomic clocks, leading into molecular metrology and tests of fundamental physics. The latter opens the field of ultracold chem