The Herschel Multi-tiered Extragalactic Survey (HerMES) is the largest Guaranteed Time Key Programme on the Herschel Space Observatory. With a wedding cake survey strategy, it consists of nested fields with varying depth and area totalling ~380 deg^2. In this paper, we present deep point source catalogues extracted from Herschel-SPIRE observations of all HerMES fields, except for the later addition of the 270 deg^2 HeLMS field. These catalogues constitute the second Data Release (DR2) made in October 2013. A subset of these catalogues, which consists of bright sources extracted from Herschel-SPIRE observations completed by May 1, 2010 (covering ~ 74 deg^2) were released earlier in the first extensive Data Release (DR1) in March 2012. Two different methods are used to generate the point source catalogues, the SUSSEXtractor (SXT) point source extractor used in two earlier data releases (EDR and EDR2) and a new source detection and photometry method. The latter combines an iterative source detection algorithm, StarFinder (SF), and a De-blended SPIRE Photometry (DESPHOT) algorithm. We use end-to-end Herschel-SPIRE simulations with realistic number counts and clustering properties to characterise basic properties of the point source catalogues, such as the completeness, reliability, photometric and positional accuracy. Over 500, 000 catalogue entries in HerMES fields (except HeLMS) are released to the public through the HeDAM website (http://hedam.oamp.fr/herMES).
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