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The list does not need to be read linearly or only one book at a time. It is encouraged to go between books and read several at a time to acquire the necessary language and understand the motivations.
The list does not need to be read linearly or only one book at a time. It is encouraged to go between books and read several at a time to acquire the necessary language and understand the motivations.


The "Royal Road to Differential Geometry and Physics" is the focus of the list. While on that track, you should refer to the "Fill in Gaps" and "Backbone" sections as needed.
The '''Royal Road to Differential Geometry and Physics''' is the focus of the list. While on that track, you should refer to the "Fill in Gaps" and "Backbone" sections as needed.


The "Fill in Gaps" section covers the knowledge acquired in a strong high school mathematics education. Refer to it as needed, or begin there to develop your core skills.
The '''Fill in Gaps''' section covers the knowledge acquired in a strong high school mathematics education. Refer to it as needed, or begin there to develop your core skills.


The "Backbone" section supports the ideas in the "Royal Road". Refer to it to strengthen your understanding of the ideas in the main track and to take those ideas further.
The '''Backbone''' section supports the ideas in the '''Royal Road'''. Refer to it to strengthen your understanding of the ideas in the main track and to take those ideas further.


The greatest hurdles are motivation and coming to understand the language of mathematics.
The greatest hurdles are motivation and coming to understand the language of mathematics.