* FTSEurofirst 300 up 0.3 pct, Euro STOXX 50 up 0.6 pct
* FTSEurofirst just few points shy of near 2-year high
* Volumes thin as Wall Street closed for holiday
* Third of euro zone blue chips still trade below book value
PARIS, Jan 21 (Reuters) - European shares rose on Monday, climbing back towards near two-year highs, with investors buying into relatively 'undervalued' sectors such as utilities and steel as they bet Europe's economy will improve.
A sell-off in luxury stocks capped gains, however, sparked by comments from Swiss watch maker Richemont about weak sales growth in China. Its shares lost 5.6 percent, while Burberry dropped 1.4 percent and Louis Vuitton owner LVMH fell 1 percent.
The FTSEurofirst 300 index of top European shares ended 0.3 percent higher at 1,166.53 points, just a few points shy of a near-two-year high of 1,170.29 hit on Jan. 10.
The euro zone's blue chip Euro STOXX 50 index added 0.6 percent to 2,726.63 points, moving back towards an 18-month high hit a week ago, while Britain's FTSE 100 index rose 0.4 percent and hit a 4-1/2 year high.
Trading volume was low in Europe on Monday as Wall Street was closed for Martin Luther King Jr. Day.
Shares of utilities and basic resources companies - which were among the worst performers in Europe in 2012 - led the gainers on Monday, with ArcelorMittal surging 4 percent, GDF Suez adding 1.8 percent and E.ON climbing 1.6 percent.
"Investors are switching to the 'value' stocks, they're looking for the cheapest valuations. If things finally improve on the macro side in Europe, these are the stocks that could outperform, after years of underperformance," a Paris-based trader said.
The STOXX Europe 600 utility sector index lost 1 percent last year and the STOXX Europe 600 basic resources sector index gained 3.9 percent, both strongly underperforming the broad STOXX Europe 600 benchmark, which gained 14 percent on the year.
Investors have been scooping up European shares in the past two months - with the Euro STOXX 50 surging 13 percent since mid-November - as fears about a potential break up of the euro zone abated and global macroeconomic data improved.
"The stress is coming down in Europe," Barclays France director Franklin Pichard said.
"Bond yields are falling in Southern Europe, while there's a bit of tension on German and French 10-year bond yields. Could this finally be the start of reallocation out of bonds from Northern Europe countries and into equities?"
According to EPFR Global data, flows going into equity funds outpaced flows going into bond funds for a fifth straight week in the week ending Jan. 16, with equity funds attracting money from retail investors for a second week running.
Despite the brisk two-month rally, European equities remain relatively cheap, with about a third of the stocks listed on the Euro STOXX 50 still trading below their book value, according to Thomson Reuters data.
The asset class is also seen as attractive relative to bonds, with an average dividend yield of 3.5 percent while the Bund yield is around 1.5 percent, a 200 basis point spread.
The spread has tightened since hitting a record high of 280 basis points last June, but remains well above historical levels.