The ''deep battle'' is something of an anachronism these days of 'Hybrid War'. Or do I mean '3 Block War'? Anyway, whatever the latest (US) government approved model of warfare is today.
In essence, the 'deep battle' was all about what we'd like to do to the enemy that lay beyond our immediate grip in the 'close battle' - its corollary in many ways. The basic premise is that we seek to 'shape' the enemy in his depth (surely our depth as well) before doing 'something decisive'.
This 'something' and that 'shaping' essentially forms the core of what we old duffers do at Staff College - except that we dress it up using polysyllabic nonsense-words to make it look like we know what we're talking about (hint: we dont - that's why we have very bright Chiefs of Staff...). In theory, we would then be decisive, the enemy would be completely unhinged (and hopefully be irretrievably disclocated with his moral determination to fight weakened...) and we would all go home to tea and medals.
Anyone with half a functioning brain can see that this is an 'economy of force' tactic...and we all know what true military thinkers understand by the term 'tactic'. No shame in it being an economoy of force measure though - on that path lies true greatness.
The idea of the deep battle is still valid although has evolved beyond a literal 2-dimensional understanding of the term. One can know refer to the non-kinetic deep battle (a highly saleable concept in my view), the idea of an entirely white-force focussed deep operations campaign (note: delivered by 'spin doctors', usually about 18 months before an election) and can even be used in a domestic setting...getting a beer pass to the pub will usually require some investment in deep operations with the long-haired CO...