To advance one week:
MyObject.MyDate + 7
To advance one year:
DATE(DAY_OF_MONTH(MyObject.MyDate), MONTH(MyObject.MyDate), YEAR(MyObject.MyDate) + 1)
You can also use function DATE for advancing months by incrementing the month parameter. Functions like LAST_DAY_OF_MONTH, LAST_DAY_OF_NEXT_MONTH, and others may be useful if you need to take special care when advancing end-of-month dates, like the 31st.