1. A cognitive training system comprising: (a) a processor configured to present cognitive training to a user, said processor being further configured to store user parameters and adjust values of exercise and training parameters at least partially in accordance with and responsive to said stored user parameters; (b) at least one training program contained within at least one computer module associated with a series of training components; (c) a visual display and an audio transducer configured to be operated upon by the processor to present visual and auditory stimuli in accordance with said adjusted exercise and training parameters; and, (d) a user interface module for allowing the user to provide user input to said processor responsive to at least one specified of said training components transmitted to said visual display and audio transducer from said processor, said processor being further configured to: (i) provide as a first training component, an audio-visual presentation of an animation having contained therein said audio and visual stimuli according to a theme that reinforces a cognitive pairing association of said visual and auditory stimuli and does not require a behavioral response from the user; (ii) present to the user responsive to (1) said user parameters, or (2) said adjusted values of exercise and training parameters, at least one second training component having the same stimuli as presented in the first training component and selected from the group: a. at least one of an auditory cue through said audio transducer and a visual cue through a visual display in order to realize a specific exercise training component; and b. at least one cross-modal cue, in a different modality than the auditory or visual cue previously presented, said cross-modal cue selected as a function of said previously presented cue; (iii) present to the user at least one of an auditory and a visual probe stimulus; (iv) obtain user input responsive to a task presented to the user related to at least one of the auditory and a visual probe stimuli, as part of the second training component; (v) store and evaluate the user input as user input data, and based upon the evaluation of user input data provide the user with feedback selected from the set of feedback types including at least positive feedback, no feedback, and neutral feedback; and in the case of neutral feedback then requesting that the user to “try again” by providing up to N additional user input responses, where N is set to 2 or 3; and (vi) adjust subsequent training level of the user based upon the evaluation input data assessed for all user input made for the at least one second training component, wherein if a selected performance rate of correct answers is met then the training level may be increased.