Discuss the issues that led to the Marbury v. Madison case of 1803. What were the results of the decision, and what impact did it have on the Supreme Court and the country?

This landmark case came out of the bitter political dispute between the outgoing Federalist Administration led by President Adams and the incoming Democratic-Republican Administration led by the new president, Thomas Jefferson. After going down to defeat in the 1800 election, the Federalists wanted to stymie the Democratic-Republicans' legislative agenda by packing the judiciary with their appointees. One of these men was a man called William Marbury.
Unfortunately for him, he didn't receive the letter confirming his judicial appointment in time, so he wasn't given his promised position as judge. Incensed at being deprived at what he considered was rightfully his, he sued the new Administration, in the person of the Secretary of State, James Madison.
The Supreme Court had to maintain a very delicate balance in this case. It consisted overwhelming of Federalist supporters of the outgoing Adams Administration. And though they were inevitably hostile to the new government, the justices of the Court recognized that if they displayed overt partisanship in reaching their decision, then the Democratic-Republican controlled Congress would almost certainly clip its wings.
So in his landmark decision, Chief Justice Marshall cleverly gave with one hand, but took with the other. Marbury would not be awarded his judicial commission, despite the actions of the new Administration being unlawful. In handing down this decision, the Court was invalidating the statute which had given it the power to decide this case in the first place. So on the face of it, although the Administration had won the case, at the same time the Supreme Court had given itself the power to strike down legislation it deemed unconstitutional, the power of judicial review, which it has held ever since.
https://www.oyez.org/cases/1789-1850/5us137

In the election of 1800, Thomas Jefferson of the Democratic-Republican Party defeated John Adams of the Federalist Party. John Adams wanted to ensure that the judiciary would continue to have many judges who were more supportive of views of the Federalists. Thus, just before his term ended, he appointed many Federalist judges—an action which was called the Midnight Appointments. However, not all of the judges had their commissions delivered before John Adams' presidency ended. Thomas Jefferson told his Secretary of State, James Madison, not to deliver the commissions of the judges who were in this category.
William Marbury was one of these judges. He sued, and the Supreme Court heard the case. The Supreme Court ruled that it was acceptable that these commissions were not delivered. The most important part of this decision was that the Supreme Court said it had the power of judicial review. This meant that the Supreme Court could determine if a law or action was constitutional. This has given much power to the Supreme Court, since it can strike down a law that it views as unconstitutional. When laws are passed, Congress needs to work to be sure that they will be viewed as constitutional. There have been many instances in which the Supreme Court ruled that a law was not constitutional, such as with the National Industrial Recovery Act and the Agricultural Adjustment Act, which were laws passed during the New Deal.