diff --git a/Project.toml b/Project.toml
index 2cabbc4f3..a9c2f44b2 100644
--- a/Project.toml
+++ b/Project.toml
@@ -8,6 +8,7 @@ ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
 ConcreteStructs = "2569d6c7-a4a2-43d3-a901-331e8e4be471"
 DocStringExtensions = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
 EnumX = "4e289a0a-7415-4d19-859d-a7e5c4648b56"
+EnzymeCore = "f151be2c-9106-41f4-ab19-57ee4f262869"
 FastLapackInterface = "29a986be-02c6-4525-aec4-84b980013641"
 GPUArraysCore = "46192b85-c4d5-4398-a991-12ede77f4527"
 InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
@@ -30,6 +31,7 @@ UnPack = "3a884ed6-31ef-47d7-9d2a-63182c4928ed"
 
 [weakdeps]
 BlockDiagonals = "0a1fb500-61f7-11e9-3c65-f5ef3456f9f0"
+Enzyme = "7da242da-08ed-463a-9acd-ee780be4f1d9"
 CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
 HYPRE = "b5ffcf37-a2bd-41ab-a3da-4bd9bc8ad771"
 IterativeSolvers = "42fd0dbc-a981-5370-80f2-aaf504508153"
@@ -42,6 +44,7 @@ Pardiso = "46dd5b70-b6fb-5a00-ae2d-e8fea33afaf2"
 [extensions]
 LinearSolveBlockDiagonalsExt = "BlockDiagonals"
 LinearSolveCUDAExt = "CUDA"
+LinearSolveEnzymeExt = "Enzyme"
 LinearSolveHYPREExt = "HYPRE"
 LinearSolveIterativeSolversExt = "IterativeSolvers"
 LinearSolveKernelAbstractionsExt = "KernelAbstractions"
@@ -78,6 +81,8 @@ julia = "1.6"
 
 [extras]
 BlockDiagonals = "0a1fb500-61f7-11e9-3c65-f5ef3456f9f0"
+Enzyme = "7da242da-08ed-463a-9acd-ee780be4f1d9"
+FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 HYPRE = "b5ffcf37-a2bd-41ab-a3da-4bd9bc8ad771"
 InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
@@ -95,4 +100,4 @@ SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["Test", "IterativeSolvers", "InteractiveUtils", "JET", "KrylovKit", "Pkg", "Random", "SafeTestsets", "MultiFloats", "ForwardDiff", "HYPRE", "MPI", "MKL_jll", "BlockDiagonals"]
+test = ["Test", "IterativeSolvers", "InteractiveUtils", "JET", "KrylovKit", "Pkg", "Random", "SafeTestsets", "MultiFloats", "ForwardDiff", "HYPRE", "MPI", "MKL_jll", "BlockDiagonals", "Enzyme", "FiniteDiff"]
diff --git a/ext/LinearSolveEnzymeExt.jl b/ext/LinearSolveEnzymeExt.jl
new file mode 100644
index 000000000..607189e10
--- /dev/null
+++ b/ext/LinearSolveEnzymeExt.jl
@@ -0,0 +1,166 @@
+module LinearSolveEnzymeExt
+
+using LinearSolve
+using LinearSolve.LinearAlgebra
+isdefined(Base, :get_extension) ? (import Enzyme) : (import ..Enzyme)
+
+
+using Enzyme
+
+using EnzymeCore
+
+function EnzymeCore.EnzymeRules.augmented_primal(config, func::Const{typeof(LinearSolve.init)}, ::Type{RT}, prob::EnzymeCore.Annotation{LP}, alg::Const; kwargs...) where {RT, LP <: LinearSolve.LinearProblem}
+    res = func.val(prob.val, alg.val; kwargs...)
+    dres = if EnzymeRules.width(config) == 1
+        func.val(prob.dval, alg.val; kwargs...)
+    else
+        ntuple(Val(EnzymeRules.width(config))) do i
+            Base.@_inline_meta
+            func.val(prob.dval[i], alg.val; kwargs...)
+        end
+    end
+    d_A = if EnzymeRules.width(config) == 1
+        dres.A
+    else
+        (dval.A for dval in dres)
+    end
+    d_b = if EnzymeRules.width(config) == 1
+        dres.b
+    else
+        (dval.b for dval in dres)
+    end
+
+
+    prob_d_A = if EnzymeRules.width(config) == 1
+        prob.dval.A
+    else
+        (dval.A for dval in prob.dval)
+    end
+    prob_d_b = if EnzymeRules.width(config) == 1
+        prob.dval.b
+    else
+        (dval.b for dval in prob.dval)
+    end
+
+    return EnzymeCore.EnzymeRules.AugmentedReturn(res, dres, (d_A, d_b, prob_d_A, prob_d_b))
+end
+
+function EnzymeCore.EnzymeRules.reverse(config, func::Const{typeof(LinearSolve.init)}, ::Type{RT}, cache, prob::EnzymeCore.Annotation{LP}, alg::Const; kwargs...) where {RT, LP <: LinearSolve.LinearProblem}
+    d_A, d_b, prob_d_A, prob_d_b = cache
+
+    if EnzymeRules.width(config) == 1
+        if d_A !== prob_d_A
+            prob_d_A .+= d_A
+            d_A .= 0
+        end
+        if d_b !== prob_d_b
+            prob_d_b .+= d_b
+            d_b .= 0
+        end
+    else
+        for i in 1:EnzymeRules.width(config)
+            if d_A !== prob_d_A[i]
+                prob_d_A[i] .+= d_A[i]
+                d_A[i] .= 0
+            end
+            if d_b !== prob_d_b[i]
+                prob_d_b[i] .+= d_b[i]
+                d_b[i] .= 0
+            end
+        end
+    end
+
+    return (nothing, nothing)
+end
+
+# y=inv(A) B
+#   dA −= z y^T  
+#   dB += z, where  z = inv(A^T) dy
+function EnzymeCore.EnzymeRules.augmented_primal(config, func::Const{typeof(LinearSolve.solve!)}, ::Type{RT}, linsolve::EnzymeCore.Annotation{LP}; kwargs...) where {RT, LP <: LinearSolve.LinearCache}
+    res = func.val(linsolve.val; kwargs...)
+
+    dres = if EnzymeRules.width(config) == 1
+        deepcopy(res)
+    else
+        ntuple(Val(EnzymeRules.width(config))) do i
+            Base.@_inline_meta
+            deepcopy(res)
+        end
+    end
+
+    if EnzymeRules.width(config) == 1
+        dres.u .= 0
+    else
+        for dr in dres
+            dr.u .= 0
+        end
+    end
+
+    resvals = if EnzymeRules.width(config) == 1
+        dres.u
+    else
+        ntuple(Val(EnzymeRules.width(config))) do i
+            Base.@_inline_meta
+            dres[i].u
+        end
+    end
+
+    dAs = if EnzymeRules.width(config) == 1
+        (linsolve.dval.A,)
+    else
+        ntuple(Val(EnzymeRules.width(config))) do i
+            Base.@_inline_meta
+            linsolve.dval[i].A
+        end
+    end
+
+    dbs = if EnzymeRules.width(config) == 1
+        (linsolve.dval.b,)
+    else
+        ntuple(Val(EnzymeRules.width(config))) do i
+            Base.@_inline_meta
+            linsolve.dval[i].b
+        end
+    end
+
+    cachesolve = deepcopy(linsolve.val)
+
+    cache = (copy(res.u), resvals, cachesolve, dAs, dbs)
+    return EnzymeCore.EnzymeRules.AugmentedReturn(res, dres, cache)
+end
+
+function EnzymeCore.EnzymeRules.reverse(config, func::Const{typeof(LinearSolve.solve!)}, ::Type{RT}, cache, linsolve::EnzymeCore.Annotation{LP}; kwargs...) where {RT, LP <: LinearSolve.LinearCache}
+    y, dys, _linsolve, dAs, dbs = cache
+
+    @assert !(typeof(linsolve) <: Const)
+    @assert !(typeof(linsolve) <: Active)
+
+    if EnzymeRules.width(config) == 1
+        dys = (dys,)
+    end
+
+    for (dA, db, dy) in zip(dAs, dbs, dys)
+        z = if _linsolve.cacheval isa Factorization
+            _linsolve.cacheval' \ dy
+        elseif _linsolve.cacheval isa Tuple && _linsolve.cacheval[1] isa Factorization
+            _linsolve.cacheval[1]' \ dy
+        elseif _linsolve.alg isa AbstractKrylovSubspaceMethod
+            # Doesn't modify `A`, so it's safe to just reuse it
+            invprob = LinearSolve.LinearProblem(transpose(_linsolve.A), dy)
+            solve(invprob;
+                abstol = _linsolve.val.abstol,
+                reltol = _linsolve.val.reltol,
+                verbose = _linsolve.val.verbose)
+        else
+            error("Algorithm $(_linsolve.alg) is currently not supported by Enzyme rules on LinearSolve.jl. Please open an issue on LinearSolve.jl detailing which algorithm is missing the adjoint handling")
+        end 
+
+        dA .-= z * transpose(y)
+        db .+= z
+        dy .= eltype(dy)(0)
+    end
+
+    return (nothing,)
+end
+
+end
\ No newline at end of file
diff --git a/src/init.jl b/src/init.jl
index 2dccda626..360a2c86e 100644
--- a/src/init.jl
+++ b/src/init.jl
@@ -15,5 +15,8 @@ function __init__()
         @require MKL_jll="856f044c-d86e-5d09-b602-aeab76dc8ba7" begin
             include("../ext/LinearSolveMKLExt.jl")
         end
+        @require Enzyme="7da242da-08ed-463a-9acd-ee780be4f1d9" begin
+            include("../ext/LinearSolveEnzymeExt.jl")
+        end
     end
 end
diff --git a/test/basictests.jl b/test/basictests.jl
index 42f283173..888f6322e 100644
--- a/test/basictests.jl
+++ b/test/basictests.jl
@@ -202,7 +202,7 @@ end
         end
     end
 
-    test_algs = if VERISON >= v"1.9"
+    test_algs = if VERSION >= v"1.9"
         (LUFactorization(),
             QRFactorization(),
             SVDFactorization(),
diff --git a/test/enzyme.jl b/test/enzyme.jl
new file mode 100644
index 000000000..62904c055
--- /dev/null
+++ b/test/enzyme.jl
@@ -0,0 +1,125 @@
+using Enzyme, ForwardDiff
+using LinearSolve, LinearAlgebra, Test
+
+n = 4
+A = rand(n, n);
+dA = zeros(n, n);
+b1 = rand(n);
+db1 = zeros(n);
+
+function f(A, b1; alg = LUFactorization())
+    prob = LinearProblem(A, b1)
+
+    sol1 = solve(prob, alg)
+
+    s1 = sol1.u
+    norm(s1)
+end
+
+f(A, b1) # Uses BLAS
+
+Enzyme.autodiff(Reverse, f, Duplicated(copy(A), dA), Duplicated(copy(b1), db1))
+
+dA2 = ForwardDiff.gradient(x->f(x,eltype(x).(b1)), copy(A))
+db12 = ForwardDiff.gradient(x->f(eltype(x).(A),x), copy(b1))
+
+@test dA ≈ dA2
+@test db1 ≈ db12
+
+A = rand(n, n);
+dA = zeros(n, n);
+dA2 = zeros(n, n);
+b1 = rand(n);
+db1 = zeros(n);
+db12 = zeros(n);
+
+#=
+# Batch test fails
+# Captured in MWE: https://github.com/EnzymeAD/Enzyme.jl/issues/1075
+
+function fbatch(y, A, b1; alg = LUFactorization())
+    prob = LinearProblem(A, b1)
+
+    sol1 = solve(prob, alg)
+
+    s1 = sol1.u
+    y[1] = norm(s1)
+    nothing
+end
+
+y = [0.0]
+dy1 = [1.0]
+dy2 = [1.0]
+Enzyme.autodiff(Reverse, fbatch, BatchDuplicated(y, (dy1, dy2)), BatchDuplicated(copy(A), (dA, dA2)), BatchDuplicated(copy(b1), (db1, db12)))
+
+dA2 = ForwardDiff.gradient(x->f(x,eltype(x).(b1)), copy(A))
+db12 = ForwardDiff.gradient(x->f(eltype(x).(A),x), copy(b1))
+
+@test_broken dA ≈ dA_2
+@test_broken dA2 ≈ dA_2
+@test_broken db1 ≈ db1_2
+@test_broken db12 ≈ db1_2
+=#
+
+function f(A, b1, b2; alg = LUFactorization())
+    prob = LinearProblem(A, b1)
+    cache = init(prob, alg)
+    s1 = copy(solve!(cache).u)
+    cache.b = b2
+    s2 = solve!(cache).u
+    norm(s1 + s2)
+end
+
+A = rand(n, n);
+dA = zeros(n, n);
+b1 = rand(n);
+db1 = zeros(n);
+b2 = rand(n);
+db2 = zeros(n);
+
+f(A, b1, b2)
+Enzyme.autodiff(Reverse, f, Duplicated(copy(A), dA), Duplicated(copy(b1), db1), Duplicated(copy(b2), db2))
+
+dA2 = ForwardDiff.gradient(x->f(x,eltype(x).(b1),eltype(x).(b2)), copy(A))
+db12 = ForwardDiff.gradient(x->f(eltype(x).(A),x,eltype(x).(b2)), copy(b1))
+db22 = ForwardDiff.gradient(x->f(eltype(x).(A),eltype(x).(b1),x), copy(b2))
+
+@test dA ≈ dA2
+@test db1 ≈ db12
+@test db2 ≈ db22
+
+function f2(A, b1, b2; alg = RFLUFactorization())
+    prob = LinearProblem(A, b1)
+    cache = init(prob, alg)
+    s1 = copy(solve!(cache).u)
+    cache.b = b2
+    s2 = solve!(cache).u
+    norm(s1 + s2)
+end
+
+f2(A, b1, b2)
+dA = zeros(n, n);
+db1 = zeros(n);
+db2 = zeros(n);
+Enzyme.autodiff(Reverse, f2, Duplicated(copy(A), dA), Duplicated(copy(b1), db1), Duplicated(copy(b2), db2))
+
+@test dA ≈ dA2
+@test db1 ≈ db12
+@test db2 ≈ db22
+
+#=
+function f3(A, b1, b2; alg = KrylovJL_GMRES())
+    prob = LinearProblem(A, b1)
+    cache = init(prob, alg)
+    s1 = copy(solve!(cache).u)
+    cache.b = b2
+    s2 = solve!(cache).u
+    norm(s1 + s2)
+end
+
+Enzyme.autodiff(Reverse, f3, Duplicated(copy(A), dA), Duplicated(copy(b1), db1), Duplicated(copy(b2), db2))
+
+@test dA ≈ dA2 atol=5e-5
+@test db1 ≈ db12
+@test db2 ≈ db22
+=#
\ No newline at end of file
diff --git a/test/runtests.jl b/test/runtests.jl
index 036bcf97e..4f2e78feb 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -8,11 +8,12 @@ const HAS_EXTENSIONS = isdefined(Base, :get_extension)
 
 if GROUP == "All" || GROUP == "Core"
     @time @safetestset "Basic Tests" include("basictests.jl")
-    @time @safetestset "Re-solve" include("resolve.jl")
+    VERSION >= v"1.9" && @time @safetestset "Re-solve" include("resolve.jl")
     @time @safetestset "Zero Initialization Tests" include("zeroinittests.jl")
     @time @safetestset "Non-Square Tests" include("nonsquare.jl")
     @time @safetestset "SparseVector b Tests" include("sparse_vector.jl")
     @time @safetestset "Default Alg Tests" include("default_algs.jl")
+    VERSION >= v"1.9" && @time @safetestset "Enzyme Derivative Rules" include("enzyme.jl")
     @time @safetestset "Traits" include("traits.jl")
 end