The June 2011 issue of Sky & Telescope discusses the two bright, easy eclipsing binary stars that are visible from the Northern Hemisphere from May through July or later: Beta Lyrae and Delta Librae. Both of these are readily visible to the unaided eye in reasonably dark skies, and both vary in brightness by roughly a full magnitude. That makes them ideal complements to Algol, the greatest eclipsing binary of all, which is too low for most northerners to observe during this time period.
The Northern Hemisphere's summer sky contains hundreds of other known eclipsing binaries, but most of these are either visible only with optical aid or vary by very small amounts — like Sigma Aquilae, which varies from magnitude 5.14 to 5.34.
The tables of predicted minima in the June issue are based on heliocentric ephemerides: a date when the star was presumed to be at minimum as seen from the Sun, together with an orbital period. The predictions have to be corrected for Earth's position; when Earth is between the Sun and the target star, we see the star's minima 8 minutes before an imaginary observer on the Sun would.
The ephemerides for Delta Librae come from the General Catalogue of Variable Stars:
Min. = JD 2442960.6994 + 2.3273543E
where E is any integer and JD is a Julian Date
These yield predictions 10 minutes earlier than those of J. M. Kreiner, another well-known and reliable source.
The ephemerides for Beta Lyrae are more complex, because this star's orbital period is gradually lengthening. We used a formula from Astronomy & Astrophysics magazine:
Min. = JD 2408247.966 + 12.913780E + 0.00000387196E2, where E is any integer.
Reliable minima of Beta Lyrae are hard to compute because the minimum is long and vague, unlike Delta Lyrae's which is momentary, and because the period is constantly changing.