Can you gain Canadian citizenship without giving up US citizenship?

Yes.

There are about 400,000 people with dual Canadian and US citizenship. This can include those born in one country whose parents have citizenship in the other, or those who obtained citizenship through naturalization.

In order to gain Canadian citizenship you would need to obtain permanent residency in Canada, live there for three out of the previous four years, apply for citizenship, pass language and Canadian knowledge tests, and then give a citizenship oath.

The issue is that most people are not able to qualify for permanent residency in Canada. You need to meet specific requirements such as: marrying a Canadian willing to sponsor you; having a skilled job offer in specific professions and then completing for one of 5,000 positions based on education, age, work experience, language skills, etc.; having a net worth of $1.6M and investing $800k in Canada; completing certain university degrees in Canada and finding a skilled work in your profession shortly after graduating; being nominated by one of the provinces (doctor willing to work in a remote community, buy and run a farm in certain provinces, world-class performing artist or athlete, etc.); etc. You must pass background, medical, and financial checks. The process can also take three to five years.

About 9,500 Americans gain permanent residency status in Canada each year. Over 70% are through family sponsorships (i.e. they marry a Canadian willing to sponsor them or are a dependent child of someone who marries a Canadian). For most people, if you have the advanced university degrees, educations, savings, etc. to immigrated to Canada, you'd already have a good life in the United States as a top doctor, nurse, business person, engineer, etc.

Both US & Canada have no laws against dual citizenship. If you ever did qualify for Canadian citizenship & got it, you would still be a US citizen. You could only enter & exit US on your currently valid US passport. You'd need your Canadian passport to enter/exit Canada.

And you would remain subject to US tax laws. US taxes all "US persons" - citizens, green card holders, and certain others - on worldwide income from all sources regardless of residence in or out of US. So you'd still be stuck in the US Tax Trap & have to file both US & Canada taxes if you got Canadian citizenship & lived/worked in Canada.

Of course.

Canada not only allows but openly encourages multiple citizenship, and the US doesn't recognize it, so none of these countries have a problem with it.

if you meet the criteria you can eventually get Canadian citizenship and retain the US citizenship

Yes, if your intent is to retain your US citizenship, you would not lose it by taking another citizenship.

Official info here: http://travel.state.gov/law/citizenship/citizenshi...

Yes.