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[I decided my previous answer was long enough, so I'm adding this one separately and making it Community Wiki. Feel free to add to it!]

Other people's PhD theses that have nice expositions on Shimura curves include:

David Helm (Berkeley 2003)
Bruce Jordan (Harvard 1981)
David Roberts (Harvard 1989)
Victor Rotger Cerda (Universitat de Barcelona 2002)
John Voight (Berkeley 2005)

[Edit (Emerton):] Ken Ribet's Inventiones 100 article describes certain instances of Shimura curves over $\mathbb Q$, including some relations with orders in quaternion algebras, and some information about $p$-adic uniformization and their bad reduction at primes describing the discriminant. Like all of Ribet's papers, it a masterpiece of exposition.

[I decided my previous answer was long enough, so I'm adding this one separately and making it Community Wiki. Feel free to add to it!]

Other people's PhD theses that have nice expositions on Shimura curves include:

David Helm (Berkeley 2003)
Bruce Jordan (Harvard 1981)
David Roberts (Harvard 1989)
Victor Rotger Cerda (Universitat de Barcelona 2002)
John Voight (Berkeley 2005)

[Edit (Emerton):] Ken Ribet's Inventiones 100 article describes certain instances of Shimura curves over $\mathbb Q$, including some relations with orders in quaternion algebras, and some information about $p$-adic uniformization and their bad reduction at primes describing the discriminant. Like all of Ribet's papers, it is a masterpiece of exposition.

[I decided my previous answer was long enough, so I'm adding this one separately and making it Community Wiki. Feel free to add to it!]

Other people's PhD theses that have nice expositions on Shimura curves include:

David Helm (Berkeley 2003)
Bruce Jordan (Harvard 1981)
David Roberts (Harvard 1989)
Victor Rotger Cerda (Universitat de Barcelona 2002)
John Voight (Berkeley 2005)

[Edit (Emerton):] Ken Ribet's Inventiones 100 article describes certain instatnces of Shimura curves over $\mathbb Q$, including some relations with orders in quaternion algebras, and some information about $p$-adic uniformization and their bad reduction at primes describing the discriminant. Like all of Ribet's papers, it a masterpiece of exposition.

[I decided my previous answer was long enough, so I'm adding this one separately and making it Community Wiki. Feel free to add to it!]

Other people's PhD theses that have nice expositions on Shimura curves include:

David Helm (Berkeley 2003)
Bruce Jordan (Harvard 1981)
David Roberts (Harvard 1989)
Victor Rotger Cerda (Universitat de Barcelona 2002)
John Voight (Berkeley 2005)

[Edit (Emerton):] Ken Ribet's Inventiones 100 article describes certain instances of Shimura curves over $\mathbb Q$, including some relations with orders in quaternion algebras, and some information about $p$-adic uniformization and their bad reduction at primes describing the discriminant. Like all of Ribet's papers, it a masterpiece of exposition.

[I decided my previous answer was long enough, so I'm adding this one separately and making it Community Wiki. Feel free to add to it!]

Other people's PhD theses that have nice expositions on Shimura curves include:

David Helm (Berkeley 2003)
Bruce Jordan (Harvard 1981)
David Roberts (Harvard 1989)
Victor Rotger Cerda (Universitat de Barcelona 2002)
John Voight (Berkeley 2005)

[I decided my previous answer was long enough, so I'm adding this one separately and making it Community Wiki. Feel free to add to it!]

Other people's PhD theses that have nice expositions on Shimura curves include:

David Helm (Berkeley 2003)
Bruce Jordan (Harvard 1981)
David Roberts (Harvard 1989)
Victor Rotger Cerda (Universitat de Barcelona 2002)
John Voight (Berkeley 2005)

[Edit (Emerton):] Ken Ribet's Inventiones 100 article describes certain instatnces of Shimura curves over $\mathbb Q$, including some relations with orders in quaternion algebras, and some information about $p$-adic uniformization and their bad reduction at primes describing the discriminant. Like all of Ribet's papers, it a masterpiece of exposition.