The “虽然……，但是……” pattern
The pattern “虽然……，但是……” (suīrán..., dànshì...) joins two clauses that contrast with each other.
虽然suīránalthough
但是dànshìbut
虽然 and 但是 may be used together, or just one of them.
Basic structure
虽然 + clause 1，但是 + clause 2
Although …, …
or
Even though …, …
Examples
虽然你忘了，但是我记得
虽然suīránalthough
你忘了nǐ wàng leyou forgot
但是dànshìbut
我记得wǒ jìdeI remember
The sentence sets two opposites side by side:
你忘了 — you forgot
but:
我记得 — I remember
外边下雪了，但是不太冷
外边wàibianoutside
下雪了xià xuě leit has started snowing
但是dànshìbut
不太冷bú tài lěngnot very cold
Only 但是 is used here.
虽然觉得有点儿累，我还是走回家了
虽然suīránalthough
觉得有点儿累juéde yǒudiǎnr lèifeel a bit tired
我还是wǒ háishiI still
走回家了zǒu huí jiā lewalked home
Only 虽然 is used here; 但是 is dropped.
Quick rule
Both: 虽然 + A，但是 + B
Although A, B.
虽然 alone: 虽然 + A，B
Although A, B.
但是 alone: A，但是 + B
A, but B.
虽然你忘了，但是我记得。— Even though you forgot, I remembered.
外边下雪了，但是不太冷。— It's snowing outside, but it isn't very cold.
虽然觉得有点儿累，我还是走回家了。— Although I felt a bit tired, I still walked home.