A method to extract out of water, concentrate and reformulate fluorides, said method comprising the successive steps of: - passing a dilute aqueous fluoride solution, so that the latter successively enters by an inlet in a cavity of an electrochemical cell, comprising at least three electrodes (3, 4, 5) each subjected to an external voltage: a first electrode used for polarizing the solution, a second electrode used as an extraction electrode, indifferently as a cathode or as an anode, in contact with and polarizing positively, negatively respectively, in the range from -15V to +15V, a large specific surface area conducting material having a structure suitable to practically occupy the whole physical space available in the cavity, while being internally soaked by the solution, and a third electrode optionally used for heating up said conducting material by means of a resistive current, flows in the cavity directly through said conducting material while internally soaking the latter, so that fluorides anions are extracted on said conducting material by the so-called electrical double layer extraction or EDLE method, comes out of the cavity by an outlet of the cavity, and - releasing the extracted anions from the surface of the conducting material by turning off the applied external voltage. - passing a dilute aqueous fluoride solution, so that the latter successively enters by an inlet in a cavity of an electrochemical cell, comprising at least three electrodes (3, 4, 5) each subjected to an external voltage: a first electrode used for polarizing the solution, a second electrode used as an extraction electrode, indifferently as a cathode or as an anode, in contact with and polarizing positively, negatively respectively, in the range from -15V to +15V, a large specific surface area conducting material having a structure suitable to practically occupy the whole physical space available in the cavity, while being internally soaked by the solution, and a third electrode optionally used for heating up said conducting material by means of a resistive current, flows in the cavity directly through said conducting material while internally soaking the latter, so that fluorides anions are extracted on said conducting material by the so-called electrical double layer extraction or EDLE method, comes out of the cavity by an outlet of the cavity, and enters by an inlet in a cavity of an electrochemical cell, comprising at least three electrodes (3, 4, 5) each subjected to an external voltage: a first electrode used for polarizing the solution, a second electrode used as an extraction electrode, indifferently as a cathode or as an anode, in contact with and polarizing positively, negatively respectively, in the range from -15V to +15V, a large specific surface area conducting material having a structure suitable to practically occupy the whole physical space available in the cavity, while being internally soaked by the solution, and a third electrode optionally used for heating up said conducting material by means of a resistive current, flows in the cavity directly through said conducting material while internally soaking the latter, so that fluorides anions are extracted on said conducting material by the so-called electrical double layer extraction or EDLE method, comes out of the cavity by an outlet of the cavity, and - releasing the extracted anions from the surface of the conducting material by turning off the applied external voltage.