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Britain's Prime Minister Theresa May gestures as she delivers a speech on leaving the European Union at Lancaster House in London, Tuesday, Jan. 17, 2017.Kirsty Wigglesworth/The Associated Press

Here are the key points from Prime Minister Theresa May's Brexit speech:

Certainty: "We will provide certainty wherever we can. We are about to enter a negotiation. That means there will be give and take."

Control over laws: "That means taking control of our own affairs, as those who voted in their millions to leave the European Union demanded we must."

Stronger union: "A stronger Britain demands that we do something else – strengthen the precious union between the four nations of the United Kingdom."

Keep common travel area with Ireland: "We cannot forget that, as we leave, the United Kingdom will share a land border with the EU, and maintaining that common travel area with the Republic of Ireland will be an important priority for the U.K. in the talks ahead."

Control immigration: "We will continue to attract the brightest and the best to work or study in Britain – indeed openness to international talent must remain one of this country's most distinctive assets – but that process must be managed properly so that our immigration system serves the national interest."

Rights for EU nationals in the U.K.: "Fairness demands that we deal with another issue as soon as possible too. We want to guarantee the rights of EU citizens who are already living in Britain, and the rights of British nationals in other member states, as early as we can."

Protect workers' rights: "As we translate the body of European law into our domestic regulations, we will ensure that workers' rights are fully protected and maintained."

Free trade with EU: "So as a priority, we will pursue a bold and ambitious free trade agreement with the European Union."

Trade deals with other countries: "A global Britain must be free to strike trade agreements with countries from outside the European Union too."

Science partnerships: "We will also welcome agreement to continue to collaborate with our European partners on major science, research and technology."

Co-operation on the fight against terrorism: "A global Britain will continue to co-operate with its European partners in important areas such as crime, terrorism and foreign affairs."

Smooth Brexit: "It is in no one's interests for there to be a cliff-edge for business or a threat to stability, as we change from our existing relationship to a new partnership with the EU."