Palladium-catalyzed cyclization conditions were screened for compatibility in forming bicyclic hydroxamic acid-containing ß-lactam cores. A palladium(II)-catalyzed oxidative amidation methodology was developed and used to synthesize several bicyclic cores, including two examples of unusual aminal-containing cores. The carboxylic acid side chain could be installed via a facile oxidative cleavage of an exocyclic alkene. Various routes were explored to install a 3-amino side chain. Chapter one provides a brief history of ß-lactam antibiotics, the rise of antimicrobial resistance, methods used to combat resistance, and the syntheses of existing core structures. In chapter two efforts towards the utilization of an intramolecular Pd(0)-catalyzed cyclization between a nitroso Diels-Alder cycloadduct and the ß-lactam amide nitrogen are described. Chapter three describes the development of a diastereoselective intramolecular Pd(II)-catalyzed oxidative cyclization between pendant alkenes and the ß-lactam amide nitrogen. The exocyclic alkene that was formed could then be cleaved to give the desired carboxylic acid. Chapter four details how aminal-containing cores are accessed in two steps from allyl hydroxamates utilizing a ruthenium-catalyzed isomerization followed by Pd(II)-catalyzed oxidative cyclization. Chapter five contains progress towards 3-amino substituted hydroxamic acid-containing bicyclic ß-lactam cores and a brief summary of accomplishments.