There are three courts that you can use in IRS disputes; the U.S. Tax Court, the U.S. District Court, and the U.S. Court of Federal Claims.
The U.S. Tax Court is the only venue where you can take your case before you pay the tax. You have 90 days from the date of your Notice of Deficiency to petition the Tax Court. Do not be intimidated, many taxpayers go to tax court Per Se; meaning you will be representing yourself. Petitioning the tax court will cost you $60. If you believe that the IRS is in error, or at fault, consult your CPA, EA, or Tax Attorney for an evaluation before you attempt this on your own because there are usually other remedies available, and you will need guidance. There are no monetary limits; you can owe the IRS as little as $500 and be in disagreement, and take them to Tax Court if you like.
The other two venues require that you pay the full amount of tax before you bring your case; think of these venues as being for refund disputes.
U.S. District Court: if you have already paid the tax, and your case has gone beyond 90 days from the date of the Notice of Deficiency, and you want a jury, then you will want to take your case to the District Court. This is the only forum with a jury. You must first file a claim for refund with the IRS, and the IRS must reject your claim, then you can file suit in District Court.
U.S. Federal Court of Claims: this court hears many claims against the United States, including claims involving taxes. Your tax attorney will need a good understanding of the different circuits, it’s more for a fairness issue versus a technical issue, and the litigations will be complex and expensive. The reasoning lies in the fact that if the Supreme Court has not ruled in a similar case, the judges in the different circuits can decide the case based on precedent specific to their circuit.
District Court and the Federal Court of Claims are going to be expensive. For all of these venues you should first start by conferencing with your licensed practitioner.