How did Judge John Marshall use the case of Marbury v. Madison to expand the authority of the Supreme Court?

The Marbury vs. Madison case resulted in John Marshall (and the other justices) giving the Supreme Court the power of judicial review. Essentially, this gave the Supreme Court the power to rule on the constitutionality (or legality) of laws made by Congress.

This expands the power of the Supreme Court, as they are now able to get rid of federal laws that go against any of the rights discussed in the Bill of Rights. This concept of judicial review still plays a critical role in the Supreme Court today, as they are constantly ruling on different cases that deal with the legality of federal laws.