Section 770 is the counterweight to § 760. Subdivision (a) lists three categories of separate property: all property owned by the person before marriage; all property acquired after marriage by gift, bequest, devise or descent; and the rents, issues and profits of the property described in the section.
The third category is the one people miss. It is not only the inheritance or the pre-marital house that stays separate — the income it produces stays separate too. Rent from a flat owned before the marriage, dividends on shares received as a gift, and the growth in those assets are all separate property under this subdivision. That is a real difference from the general rule that income during marriage is community, and it is why keeping an inherited asset and its income in a separate account matters so much in practice.
What the section does not do is protect a separate asset from everything that happens to it afterwards. Where community earnings or community effort are put into a separate asset — mortgage payments from salary, a renovation, a spouse's work in a separate business — the community may acquire an interest or a right of reimbursement under other provisions, and separate funds deposited into a joint account and spent alongside community money create a tracing problem that can defeat the claim. Subdivision (b) adds a management rule: a married person may convey their separate property without the consent of their spouse, which is the opposite of the position for community real property under § 1102. Whether an asset has kept its separate character is an evidential question about records, and belongs with a family lawyer.