The steps you need to perform to complete this recipe are as follows:

1. First, investigate whether or not any geometry is invalid in the imported table. As you can see in the following query, using the ST_IsValid and ST_IsValidReason functions, we find four invalid geometries that are all invalid for the same reason—ring self-intersection:

      postgis_cookbook=# SELECT gid, name, ST_IsValidReason(the_geom) 
        FROM chp03.countries 
        WHERE ST_IsValid(the_geom)=false;

      (4 rows) 

2. Now concentrate on just one of the invalid geometries, for example, in the multipolygon geometry representing Russia. Create a table containing just the ring generating the invalidity, selecting the table using the point coordinates given in the ST_IsValidReason response in the previous step:

      postgis_cookbook=# SELECT * INTO chp03.invalid_geometries FROM ( 
        SELECT 'broken'::varchar(10) as status,
        ST_GeometryN(the_geom, generate_series(
          1, ST_NRings(the_geom)))::geometry(Polygon,4326)
        as the_geom FROM chp03.countries 
        WHERE name = 'Russia') AS foo 
        WHERE ST_Intersects(the_geom, 
          ST_SetSRID(ST_Point(143.661926,49.31221), 4326)); 

ST_MakeValid requires GEOS 3.3.0 or higher; check whether or not your system supports it using the PostGIS_full_version function as follows:

3. Now, using the ST_MakeValid function, add a new record in the previously created table with the valid version of the same geometry:

      postgis_cookbook=# INSERT INTO chp03.invalid_geometries 
      VALUES ('repaired', (SELECT ST_MakeValid(the_geom) 
      FROM chp03.invalid_geometries)); 

4. Open this geometry on your desktop GIS; the invalid geometry has just one self-intersecting ring that produces a hole in its internal. While this is accepted in the ESRI shapefile format specification (that was the original dataset you imported), the OGC standard does not allow for the self-intersecting ring, so neither does PostGIS:

5. Now, in the invalid_geometries table, you have the invalid and valid versions of the polygon. It is easy to figure out that the self-intersecting ring was removed by ST_MakeValid adding one supplementary ring to the original polygon, which resulted in a valid geometry, according to the OGC standard:

      postgis_cookbook=# SELECT status, ST_NRings(the_geom) 
      FROM chp03.invalid_geometries; 

     (2 rows)

6. Now that you have identified the problem and its solution, don't forget to fix all the other invalid geometries in the countries table by executing the following code:

      postgis_cookbook=# UPDATE chp03.countries 
      SET the_geom = ST_MakeValid(the_geom) 
      WHERE ST_IsValid(the_geom) = false;