Form 6251 is used to figure the amount, if any, of your alternative minimum tax (AMT). The AMT applies to taxpayers who have certain types of income that receive favorable treatment, or who qualify for certain deductions, under the tax law. For more information: IRS: About Form 6251
Form 8801 is used to calculate your Minimum Tax Credit for AMT that you incurred in prior tax years and to figure any credit carryforward. IRS: About Form 8801