You can take my car as provided (that)/providing 

you don't damage it.(I will lend you my car on condition that you don't damage it.)

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Although he is rich, he lives in a small house.

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He is poor and has no house, but even if he had money, he wouldn't buy a house.

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Take an umbrella in case it rains.

(It might rain, so it's a good idea to take an umbrella.)

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Despite the rain, she walked to the station. (without being affected by the rain or by being blind.)

To conclude, I want to wish you all a very happy holiday season.

You can count on me whatever you decide to do.

(No matter what your decision is, you can count on me.)

Tom is rich, whereas Jack is poor.

(Tom is rich; in contrast Jack is poor.)

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You cannot pass this test unless you work for it!

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He had severe injuries; nevertheless, he completely recovered.

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A hurricane has been announced. Therefore, air traffic will be disrupted.

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The trip is too expensive. Besides, I don't really like hot weather.

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Computers are cheaper nowadays; furthermore, they are lighter.