
Highest individual score
Chris gayle's 175*(66 balls) against Pune Warriors remains the highest individual score in IPL till date.
Highest team total

263 for 5 wkts by Royal Challengers Bangalore against Pune Warriors, built mainly around the fastest century and highest score in IPL = 175 scored by Chris Gayle, followed by some very innovative shots by AB de Villiers. RCB hit 21 sixes in their inning, another record.
246 from 20 overs is a run rate of 12.30 which Chennai Super Kings finished with against Rajasthan Royals in a match at Chepauk back on 3 April 2010. Murali Vijay was the main architect of the mammoth total, scoring amazing 127 off just 56 balls with 8 fours and as many as 11 sixes all round the park. Vijay, regarded as a test material earlier, played a chanceless innings that day and mesmerised visitors although they put up a brave fight by losing the match only by 23 runs that too thanks to superb 4 overs for just 15 runs by Doug Bollinger on one of flattest pitch you'll ever find in India.
Chennai, that day, broke their own record of 240 vs Kings XI Punjab they had scored in the first edition in 2008 at Mohali. That too was a very high scoring game with home team replying with 207 for 4 wkts.
Lowest team total
Among the best batting teams in IPL, Royal Challengers Bangalore, own this unpleasant record of lowest total in IPL, not even managing to breach fifty run mark. No batsman crossed double figure mark either. Previously, the record was owned by Rajasthan Royals for 8 seasons. In this match played at Newlands ground in Cape Town, Rajasthan Royals had managed to limit Royal Challengers to 133 but Anil Kumble's fastish leg spin proved too hot to handle for them. Former Indian captain took 5 wickets for just 5 runs in his 3.1 overs and only 3 RR batters reached double figure scores (all making exactly 11).
Articles related to RCB's shocking performance
http://www.hindustantimes.com/ipl-2017/royal-challengers-bangalore-april-23-from-highest-ipl-total-to-lowest/story-oMHfrss0ixwVZwKaHiFOvO.html
http://www.firstpost.com/sports/highest-and-lowest-scores-in-ipl-from-rcbs-collapse-vs-kkr-to-their-blitz-against-gl-3401056.html
http://indianexpress.com/article/sports/cricket/ipl-2017-10/kkr-vs-rcb-from-high-to-low-in-four-years-lowest-ipl-scores-stats-4625928/
Courtesy:sportzwiki

Highest chases in IPL
217/7 in 19.5 overs by Rajasthan vs Deccan (214/5) at Hyderabad, 24 Apr 2008.
211/4 in 18.4 overs by Chennai, vs Bangalore (205/5) at Hyderabad, 14 May 2014.
208/5 in 20.0 overs by Chennai, vs Bangalore (205/8) at Chennai, 12 Apr 2012.
206/4 in 18.5 overs by Punjab, vs Chennai (205/4) at Abu Dhabi, 18 Apr 2014.
204/2 in 18.5 overs by Bangalore, vs Punjab (203/3) at Bangalore, 16 Mar 2010.
204/2 in 18.2 overs by Punjab, vs Kolkata (200/3) at Kolkata, 4 April 2010.
197/5 in 19.4 overs by Rajasthan, vs Deccan (196/2) at Jaipur, 17 Apr 2012.
196/7 in 20.0 overs by Gujarat, vs Pune (195/3) at Pune, 29 Apr 2016.
195/4 in 19.4 overs by Chennai, vs Punjab (192/3) at Dharamsala, 18 Apr 2010.
195/5 in 14.4 overs by Mumbai, vs Rajasthan (189/4) at Mumbai, 25 May 2014.
195/3 in 19.3 overs by Bangalore, vs Pune (191/6) at Bengaluru, 7 May 2016.
194/4 in 18.0 overs by Punjab, vs Bangalore (190/3) at Mohali, 6 May 2013.
194/6 in 20.0 overs by Punjab, vs Deccan (190/4) at Mohali, 13 May 2012.
193/1 in 16.4 overs by Delhi, vs Deccan (187/4) at Hyderabad, 10 May 2012.
193/3 in 18.4 overs by Punjab, vs Rajasthan (192/5) at Sharjah, 20 Apr 2014.
193/4 in 19.1 overs by Punjab, vs Chennai (188/4) at Mohali, 13 April 2011.
192/3 in 19.1 overs by Delhi, vs Bangalore (191/5) at Bengaluru, 17 Apr 2016.
192/5 in 19.4 overs by Kolkata, vs Chennai (190/3) at Chennai, on 27 May 2012.
191/5 in 18.5 overs by Rajasthan, vs Bangalore (190/5) at Bangalore, 11 May 2014.
190/5 in 19.1 overs by Chennai, vs Delhi (185/6) at Delhi, on 19 March 2010.
190/7 in 19.2 overs by Delhi, vs Pune (187/5) at Mumbai (DY), on 17 Apr 2011.
189/4 in 19.4 overs by Hyderabad, vs Chennai (185/3) at Ranchi, 22 May 2014