It was a week in which trading in China's markets was twice halted by a circuit breaker, before the authorities decided to suspend the measure.
The Shanghai Composite closed 2% higher on Friday, but still ended the week down by about 10%.
In London, the FTSE 100 was up 55.4 points, or 0.93%, at 6,009.4.
In Frankfurt, the Dax was up 1.0%, while the Cac 40 in Paris was up 0.7%.
On Thursday, markets in Europe and the US recorded steep losses after trading in China's stock markets closed within the first 30 minutes.
The direct financial impact of lower share prices in China is moderate. There is not enough foreign investment in the Chinese market for it to be a major problem. The London consultancy Capital Economics has said foreigners own just 2% of shares.
The issue is about whether the financial turbulence shines a light on wider issues about the economic slowdown in China: is the economy heading for what's called a "hard landing", too sharp a slowdown?
China is now such a big force in the global economy that it would inevitably affect the rest of the world. It is the second largest economy and the second largest importer of both goods and commercial services.
Read more from Andrew.
Trading in China was volatile again on Friday, the first day since the suspension of the circuit breaker.
The Chinese central bank also took steps to strengthen the yuan after the currency's weakness was taken as a sign of problems for the economy.
Connor Campbell, an analyst at Spreadex, said the FTSE's rise on Friday was "nothing to write home about, especially in the context of the near 6% plunge the UK index has witnessed since Monday".
However, he added, it did mark an important moment of calm that has been largely absent since 2016 got underway, something that could help matters heading into next week.
Market attention now turns to the US unemployment figures, which are due out later on Friday.
"It takes quite something to relegate the US employment report to a footnote in this week's trading activity, but the China induced volatility seen over the past few days appears to have done the trick," said Michael Hewson from CMC Markets.
"As we come to the end of the week European equity markets look on course to post some of the worst weekly losses since the previous China induced volatility, seen last August."
The BBC's Steve Evans in Beijing, says the reason for the volatility in China's mainland markets is that  "there's a class of share buyer who treats it almost like the dog track".
But these investors cannot fight gravity, and an enormously expensive share market has been brought to heel, he says.
Anne Richards, chief investment officer at Aberdeen Asset Management, told the BBC she was "seeing inexperience" in some parts of the regulation of Chinese markets.
The addition of inexperienced investors did not help, she said. "That's not a good setup... but over time it will improve."
Dr Nikos Paltalidis, a lecturer in Finance at Durham University Business School, added the lack of experience among investors was highlighted by the fact that the first six months of 2015 saw the Chinese stock market soar by about 50%, adding that the rise in stocks was  "disconnected from economic fundamentals".
"Investors borrowed heavily to speculate on stocks, inflating a short-lived asset bubble. With volatility high in the Chinese markets investing in high-quality, dividend-paying stocks seem to be the safest strategy for the short-term," he added.
Chinese shares have risen and European markets have opened higher at the end of what has been a torrid first week of the year.