TL;DR
This paper provides an overview of key conceptual issues in quantum gravity and summarizes various proposed solutions, serving as a course outline rather than presenting new research findings.
Contribution
It offers an idiosyncratic summary of important problems and imaginative solutions in quantum gravity, based on a graduate course.
Findings
Highlights major conceptual problems in quantum gravity
Summarizes diverse proposed solutions
Provides educational insights into the field
Abstract
These are notes for a graduate course in quantum gravity planned at IFT-UAM/CSIC for the spring term of 2020, but delayed for an indefinite period of time (although a shortened version was given in the Escuela de Fisica (Institute of Physics) in the University of Costa Rica.). The aim of the course was to highlight the most important conceptual problems in the field and to summarize some of the most imaginative solutions to them that have been proposed in the literature. The course can best be characterized as idiosyncratic rather than encyclopedic.
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