In this thesis, we calculate the cooperations algebra for the second truncated Brown-Peterson spectrum, BP⟨2⟩, at the prime 2. We accomplish this through the Adams spectral sequence

Ext_A*(F₂, H_*(BP⟨2⟩

BP⟨2⟩; F₂)) ⇒ BP⟨2⟩_* BP⟨2⟩ ⊗ Z₂

We begin by introducing a filtration and a splitting of the mod 2 homology of BP⟨2⟩. From this splitting we will derive a splitting on the Ext-groups of BP⟨2⟩

BP⟨2⟩ into a &ugr;₂-torsion component, which is concentrated in Adams filtration 0, and a &ugr;₂-torsion free component. We then show that this algebraic splitting lifts to a splitting of the spectrum BP⟨2⟩

BP⟨2⟩.

After establishing our general structural results, we turn to developing an inductive procedure for determining a basis for the &ugr;₀-inverted Ext groups of BP⟨2⟩

BP⟨2⟩,and from this determine a F₂[&ugr;₀]-basis for Ext_E(2)*(F₂, H_*(BP⟨2⟩; F₂))= &ugr;₀-tors.