-te form follow with mo
 

I buy two book to learn japanese.
-te form for :
v-verb : suffix -ru is replaced by -te (-て)
c-verb : suffix -u,-tsu atau -ru is replaced by -tte (-つて)
suffix -bu, -mu atau -nu is replaced by -nde (-んで)
suffix -su is replaced by -shite (-して)
suffix -ku is replaced by -ite (-いて)
suffix -gu is replaced by -ide (-いで)
other verb : suru (する) become shite (して)
kuru (くる) become kite (きて)
iku (いく) become itte (いつて)
adjective-i : suffix -i is replaced by -kute (-くて)
adjective-na : is added with -de (-で)

the problem is when -te form is followed mo have different description.
in first book, it's said that it's for conditional.
example : Ano kaban ga takakutemo, watashi wa kaimasen.
meaning in english : if that bag is expensive, I will not buy it.
in second book, it's said that it's to express something that is against the cause/requirement/reason for the following sentence.
example : ashita ame ga futtemo, watashi wa Kooen e ikimasu.
meaning in english : Although tommorrow is raining, I will go to park.

which one is correct ? or is both of them correct ?

I like to think of it as "Even if" or "Even though" in most cases.

So for the second example sentence I would think of the translation as:
明日雨が降っても公園へ行きます。
Even if it is raining tomorrow, I'll go to the park

The thing that is slightly confusing to me is the example sentence in your first book that says
あのかばんが高くても私は買いません。
To me that should translate as "Even if that bag is expensive I won't buy it"
I even searched for 高くても買いません on google and didn't get any direct results.
In fact the results gave these kinds of sentences.

ps3が高くて買えません。
どうして高くても買ってしまうの？
高くても買いたい。

安くても買いません yielded much more accurate results, probably because 高くても買いません sounds strange to me even in English, unless you are someone who will only buy expensive things or something like that.

あのかばんが高くて買いません would make more sense to me.
Or like i said earlier あのかばんが安くても買いません。

So is it just me lacking some sort of knowledge in the use of ～ても or is the example sentence off?

No, it isn't you. It's one of the OP's books that is wrong.

The sentence あのかばんが高くても私は買いません makes absolutely no sense. :p