SWIMMING IN A POOL

Doing those things, which provide exercise to the body as exercise is permitted by the Shariah.  Swimming is not only an exercise, but Allah (Subhanahu Wa Ta'ala) forbid, in calamities like floods, etc. can be used to save one's life and others' lives.  

The Holy Prophet (Sallallahu alaihi wa sallam) has specially permitted and emphasized swimming.  
It is given in (Jame' Ul Ahadith Wal Maraseel) by Imam Jalaluddin Suyuti

Translation of Hadith:  The Holy Prophet (Sallallahu alaihi wa sallam) said: You teach your children swimming and bow shooting.  Teach your women how to knit wool.  (Jame' Ul Ahadith, Vol. 5, Pg No. 153)

There is also a Hadith in (Sunan Kubra of Imam Nasai)

Translation of Hadith:  It has been narrated on the authority of Hadhrat 'Ata Bin Abi Ribah (May Allah be well pleased with him), he said that he saw Hadhrat Jabir Bin Abdullah Ansari and Hadhrat Jabir Bin 'Ameer Ansari (May Allah be well pleased with them) bow shooting.  One of them said: I heard the Holy Prophet (Sallallahu alaihi wa sallam) say: Everything, which does not have the remembrance of Allah Ta'ala is useless, except 4: A man joking with his wife, rearing a horse, running between 2 points and swimming.  (Sunan Kubra, Vol. 5, Pg No. 302)

These Hadith show that going to a swimming pool for swimming is permissible.  However, it is not allowed to reveal any spot of the body from under the navel (belly button) to the knees.  Youngsters who swim should cover their body properly and avoid exposing their body.  

As given (Al Fiqh Alal Madhahib Al Arba, Vol. 2, Pg No. 50)