I know that there are many kinds of such caves, but I am looking for ones (if they exist, and I don't know) that contain stalagmite and stalactites and are located at high altitude inside a mountain. I also need to know in what kind of mountains they are, and what kind of rocks must be present. Also, can you suggest me a reference book about the topic? I know nearly nothing about geology.
The classic text has long been "Karst Hydrology and Physical Speleology" by Alfred Bogli, - which I highly recommend.
Karstic dissolution and precipitation (to form stalactites, helictites, etc.) are basically hydrologic processes in which groundwater seeks to attain thermodynamic equilibrium with the carbonate rocks with which it is in contact. Water flows downhill towards the base-level of erosion - generally sea level. But bear in mind that during the last glaciation sea level was about -120 metres compared to modern sea level. To get very high mountain karst the system has to develop and then be lofted by other tectonic processes of uplift. In the Jebel Akhdar of Oman there are caves up to about 2 km elevation, but I guess that some limestone massifs have been elevated higher than that.