System (S, S1) for insulating and dry cladding with limited thickness of the perimeter, with ventilated air gap, of a building wall, characterized in that it comprises: - a plurality of wall fixing brackets, - a plurality of aluminium profile, extending vertically, or - a plurality of aluminium profiles, extending horizontally, wherein each bracket is configured as an L-shaped plate and comprises: - a first wing (14.1) resting against a surface of said wall, having a plurality of holes, preferably slotted holes, and fixed securely in said wall by means of a plurality of wall plugs engaged in respective holes of said first wing (14. 1); - a second wing (14.2) arranged in a vertical plane, orthogonal with respect to said surface of said wall, projecting frontally with respect to said first wing (14.1) and having a plurality of slotted holes, wherein: - each aluminium profile (13, 23) comprises: - a first longitudinal body (13.1, 23.1); - a second longitudinal body (13.2, 23.2) aligned with respect to said first body (13.1, 23.1) according to a reference plane parallel to the front face of said wall; - an integral longitudinal intermediate rib (13.3, 23.3) joining said two bodies (13.1, 13.2; 23.1, 23.2) and which is arranged parallel to said reference plane and is opposite respective continuous longitudinal intermediate slits, a rear intermediate slit and a front intermediate slit (13.30), respectively; and wherein: - each aluminium profile (13, 23) is fixed with respect to at least two brackets and supports supporting means, or joining means, configured for fixing a plurality of external finishing panels; characterized in that the major axis of the second wing (14.2) is inclined with a descending trend from the outside towards the inside of said wall; and that the first and second longitudinal bodies (13.1, 23.1; 13.2, 23.2) are box-shaped, and that pairs of continuous linear protrusions (13.4, 23.4) are provided respectively on the external front faces of said two longitudinal box-shaped bodies (13.1, 13.2; 23.1, 23.2). - a plurality of wall fixing brackets, - a plurality of aluminium profile, extending vertically, or - a plurality of aluminium profiles, extending horizontally, L-shaped plate and comprises: - a first wing (14.1) resting against a surface of said wall, having a plurality of holes, preferably slotted holes, and fixed securely in said wall by means of a plurality of wall plugs engaged in respective holes of said first wing (14. 1); - a second wing (14.2) arranged in a vertical plane, orthogonal with respect to said surface of said wall, projecting frontally with respect to said first wing (14.1) and having a plurality of slotted holes, - a first wing (14.1) resting against a surface of said wall, having a plurality of holes, preferably slotted holes, and fixed securely in said wall by means of a plurality of wall plugs engaged in respective holes of said first wing (14. 1); - a second wing (14.2) arranged in a vertical plane, orthogonal with respect to said surface of said wall, projecting frontally with respect to said first wing (14.1) and having a plurality of slotted holes, wherein: - each aluminium profile (13, 23) comprises: - a first longitudinal body (13.1, 23.1); - a second longitudinal body (13.2, 23.2) aligned with respect to said first body (13.1, 23.1) according to a reference plane parallel to the front face of said wall; - an integral longitudinal intermediate rib (13.3, 23.3) joining said two bodies (13.1, 13.2; 23.1, 23.2) and which is arranged parallel to said reference plane and is opposite respective continuous longitudinal intermediate slits, a rear intermediate slit and a front intermediate slit (13.30), respectively; - each aluminium profile (13, 23) comprises: - a first longitudinal body (13.1, 23.1); - a second longitudinal body (13.2, 23.2) aligned with respect to said first body (13.1, 23.1) according to a reference plane parallel to the front face of said wall; - an integral longitudinal intermediate rib (13.3, 23.3) joining said two bodies (13.1, 13.2; 23.1, 23.2) and which is arranged parallel to said reference plane and is opposite respective continuous longitudinal intermediate slits, a rear intermediate slit and a front intermediate slit (13.30), respectively; - a first longitudinal body (13.1, 23.1); - a second longitudinal body (13.2, 23.2) aligned with respect to said first body (13.1, 23.1) according to a reference plane parallel to the front face of said wall; - an integral longitudinal intermediate rib (13.3, 23.3) joining said two bodies (13.1, 13.2; 23.1, 23.2) and which is arranged parallel to said reference plane and is opposite respective continuous longitudinal intermediate slits, a rear intermediate slit and a front intermediate slit (13.30), respectively; and wherein: - each aluminium profile (13, 23) is fixed with respect to at least two brackets and supports supporting means, or joining means, configured for fixing a plurality of external finishing panels; - each aluminium profile (13, 23) is fixed with respect to at least two brackets and supports supporting means, or joining means, configured for fixing a plurality of external finishing panels; characterized in that the major axis of the second wing (14.2) is inclined with a descending trend from the outside towards the inside of said wall; and that the first and second longitudinal bodies (13.1, 23.1; 13.2, 23.2) are box-shaped, and that pairs of continuous linear protrusions (13.4, 23.4) are provided respectively on the external front faces of said two longitudinal box-shaped bodies (13.1, 13.2; 23.1, 23.2).