European shares opened higher on Tuesday and were on track ​for their biggest quarterly rise in more than five years, boosted by optimism around artificial intelligence and signs of easing tensions in the Middle East. The pan-European Stoxx index rose 0.9 per cent to 641.73, just off a record high reached earlier in the session. The benchmark ​posted a third consecutive monthly gain and climbed 10.5 per cent for the quarter, its strongest such performance since October 2020.Global ​equities have rallied this quarter on artificial intelligence (AI) enthusiasm, with the US and Asia at the forefront, while Europe’s smaller exposure to the tech sector has resulted in it playing catch up for most of this period. Signs of easing Middle East tensions have also been a key driver this quarter as prices of oil slipped to pre-Iran-war levels, prompting Barclays and JP Morgan to turn bullish on European stocks.DublinThe Iseq All-Share index edged 0.2 per cent higher to 13,828.74. Ryanair rose 0.8 per cent to €27.35. Bank of United States pushed its buy recommendation on the stock in a note saying its discussions with airlines suggest European short haul bookings have improved recently.Kingspan was also in demand, rising 0.8 per cent to €79.95. However, banking stocks were mixed even as the wider sector across Europe ended in positive territory. AIB lost 1.1 per cent to €10.28, while Bank of Ireland added 0.1 per cent to €17.43. LondonThe UK’s blue-chip FTSE 100 inched 0.1 per cent higher.Of Irish interest, Grafton Group rose 0.8 per cent to £9.07 after the builders merchanting and DIY retailing company launched a £25 million (€29 million) programme to buy back its own stock. It followed the group having spent about £430 million since 2022 repurchasing and cancelling more than a fifth of its stock.Banks added 0.8 per cent and ‌were ‌up ​20 per cent for the quarter. Lloyds and NatWest gained 2.1 per cent and 1.6 per cent, respectively.Aerospace and defence stocks rose 2.1 per cent after UK prime minister Keir Starmer unveiled an extra £15 ⁠billion to modernise the UK’s depleted ​armed forces. Rolls-Royce, BAE Systems, Melrose Industries and ​Babcock were up between 2 per cent and 3.3 per cent.The UK’s biggest housebuilders are facing a potential multi-billion-pound class action lawsuit over alleged anticompetitive conduct, according to a consumer claim. The home construction index dropped, while Persimmon, Barratt Redrow and Taylor Wimpey fell between ‌1 per cent and 3 per cent.Supermarket group Sainsbury’s rose 1.3 per cent after first-quarter results but said it expects the Middle East conflict to add to food inflation.EuropeChip equipment maker ASML rose 6.8 per cent, while chipmakers STMicroelectronics and Infineon were also in demand. Shares of Siemens Energy added 5.6 per cent after the AI equipment maker ⁠reiterated strong demand trends at a quarterly earnings call ​on Monday.Travel and leisure stocks, which had taken a hit due to the conflict, also bounced back and were up over 19 per cent this quarter – their biggest ‌jump since January 2023. Among individual stocks, Abivax jumped over 38 per cent after the ​French drugmaker reported positive topline results for its obefazimod study. Among laggards, customer services ​firm Teleperformance fell after US peer Concentrix cut its profit forecast.New YorkWall Street’s main indexes were on course ‌to close June with their strongest quarterly gains in years, underscoring the resilience of equities despite geopolitical challenges and inflation concerns.The S&P 500 real estate index dropped, hurt by a decline in shares ‌of Digital Realty after the ⁠data centre REIT priced a secondary share sale.Shares of Concentrix hit a record low after the customer experience firm lowered its full-year forecasts for revenue ‌and adjusted profit.Morgan Stanley shares dipped after brokerage Oppenheimer downgraded major Wall Street investment banks, recommending that investors ​redeploy capital into alternative asset managers. – Additional reporting, Reuters