Quickly review the משנה דף ב
https://hebrewbooks.org/shas.aspx?mesechta=3&daf=2&format=pdf
Questions:
Why did the Rabanan prohibit carrying inside a מבוי?
Learn Rashi very well
How many walls are needed to create a Reshus hayachid?
Learn תוס’ רבינו פרץ
and רבינו יהונתן (in back of the gemara on side of the Rif)
https://hebrewbooks.org/pdfpager.aspx?req=14312&st=&pgnum=326
and רע”ב on the Mishna
https://hebrewbooks.org/pdfpager.aspx?req=9678&st=&pgnum=149
What is the position of the Rambam?
Learn רמב”ם הלכות שבת פרק יד הלכה א & ד
https://hebrewbooks.org/pdfpager.aspx?req=14278&st=&pgnum=57
https://hebrewbooks.org/pdfpager.aspx?req=14278&st=&pgnum=58
Learn רמב”ם הלכות שבת פרק יז הלכה ט and השגת הראב”ד
https://hebrewbooks.org/pdfpager.aspx?req=14278&st=&pgnum=73
See מגיד משנה הלכות שבת פרק יז הלכה א for an explanation of the Rambam
https://hebrewbooks.org/pdfpager.aspx?req=14278&st=&pgnum=72
See ח’ גרי”ז עירובין for the Brisker Rav’s explanation of the Rambam