Now in its fourth year, this annual festival of jazz and improvised music is better and more ambitious than ever. Programmed and presented by the Umbrella Music collective, which includes several leading lights of the local scene, it runs through Sunday at multiple venues. The festival kicks off Thursday with “European Jazz Meets Chicago,” a free fest-within-a-fest at the Cultural Center (78 E. Washington) that starts at 6 PM and features six acts in two halls. Umbrella’s partnership with Swiss, German, Dutch, Lithuanian, Swedish, and Austrian consulates and cultural organizations helped secure the participation of musicians from those nations, some of whom—like Swedish guitarist David Stackenas and Swiss reedist Hans Koch—will perform with Chicagoans. I’ve written a Critic’s Choice about Lithuanian saxophonist Liudas Mockunas and Austrian drummer Martin Brandlmayr, Thursday’s first two artists, but special attention should also be paid to brilliant Dutch pianist Guus Janssen, who plays at 10 PM in a trio with his brother Wim on drums. (Janssen also plays a free “satellite” concert, which isn’t formally part of the festival, Friday at noon in the Cultural Center’s Randolph Street Cafe.)