尽管

= although, despite, even though. (a little stronger than 虽然)

尽管 should be pronounced as “jǐn guǎn”, although many educated native speakers pronounce it exclusively as “jìn guǎn”.

尽管……，subject + （却）还是……
尽管……，但 subject + （却）还是……
尽管……，可是 subject + （却）还是……
尽管……，但是 subject + （却）还是……
尽管……，可是 subject + （却）……
尽管……，但是 subject + （却）……

= despite the fact that…, somebody still…

但是、可是、还是 are used to emphasise the shift in meaning in the second clause. At least one must be kept in the second clause.

却 shows disappointment, criticism, disgreement or unexpectedness. (See 却)

尽管很多人批评他，他还是坚持这么做。
= 尽管很多人批评他，可是他还是坚持这么做。
Despite the fact that many people criticize him, he still insists on doing it.
Note: “……，他却还是坚持这么做。” means I don’t think he should insist. I didn’t expected this. I disgree with this.

尽管困难很多，但是我们不能放弃。
= 尽管困难很多，我们还是不能放弃。
Even though there are many difficulties, we can’t just give up.
Note: “……，我们却不能放弃。” means I think we should give up. I wish we could give up.

尽管我很生气，但是我没发脾气。
= 尽管我很生气，但是我还是没发脾气。
Even though I was angry, I didn’t lose my temper.

尽管已经毕业很多年了，我们还是经常联系。
尽管已经毕业很多年了，但我们经常联系。
Although we have graduated for many years, we still keep in touch.

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