diff --git a/src/basis/abstract.jl b/src/basis/abstract.jl
index 65ad2da..af73f5a 100644
--- a/src/basis/abstract.jl
+++ b/src/basis/abstract.jl
@@ -72,3 +72,108 @@ eval_dbasis(B::AbstractBasis{dim}, xi) where {dim} = collect(eval_dbasis!(B, xi)
 function get_reference_element_coordinates end
 function eval_basis! end
 function eval_dbasis! end
+
+# ============================================================================
+# Parametric Lagrange Basis Type
+# ============================================================================
+
+"""
+    Lagrange{T<:AbstractTopology, P} <: AbstractBasis
+
+Parametric Lagrange basis functions for topology `T` with polynomial degree `P`.
+
+The node count is automatically derived from the topology and polynomial degree:
+- `Lagrange{Triangle, 1}`: P1 → 3 nodes (vertices)
+- `Lagrange{Triangle, 2}`: P2 → 6 nodes (vertices + edge midpoints)
+- `Lagrange{Quadrilateral, 1}`: Q1 → 4 nodes (corners)
+- `Lagrange{Quadrilateral, 2}`: Q2 → 9 nodes (full tensor product)
+- `Lagrange{Tetrahedron, 1}`: P1 → 4 nodes (vertices)
+- `Lagrange{Tetrahedron, 2}`: P2 → 10 nodes (vertices + edge midpoints)
+- `Lagrange{Hexahedron, 1}`: Q1 → 8 nodes (corners)
+- `Lagrange{Hexahedron, 2}`: Q2 → 27 nodes (full tensor product)
+
+# Type Parameters
+- `T`: Topology type (Triangle, Quadrilateral, Tetrahedron, Hexahedron, etc.)
+- `P`: Polynomial degree (1 = linear, 2 = quadratic, 3 = cubic, ...)
+
+# Mathematical Background
+
+Lagrange basis functions satisfy the cardinal property:
+```
+Nᵢ(xⱼ) = δᵢⱼ  (Kronecker delta)
+```
+
+where `xⱼ` are the interpolation nodes.
+
+For polynomial degree P:
+- 1D: P+1 nodes
+- Triangle: (P+1)(P+2)/2 nodes
+- Quadrilateral: (P+1)² nodes (tensor product)
+- Tetrahedron: (P+1)(P+2)(P+3)/6 nodes
+- Hexahedron: (P+1)³ nodes (tensor product)
+
+# Example
+
+```julia
+# Linear triangle (P1)
+basis = Lagrange{Triangle, 1}()
+nnodes(basis)  # → 3
+
+# Quadratic triangle (P2)
+basis = Lagrange{Triangle, 2}()
+nnodes(basis)  # → 6
+
+# Bilinear quadrilateral (Q1)
+basis = Lagrange{Quadrilateral, 1}()
+nnodes(basis)  # → 4
+
+# Biquadratic quadrilateral (Q2)
+basis = Lagrange{Quadrilateral, 2}()
+nnodes(basis)  # → 9
+```
+
+See also: [`AbstractBasis`](@ref), [`Serendipity`](@ref), [`Nedelec`](@ref)
+"""
+# Lagrange inherits from AbstractBasis but dimension is determined by topology
+# We cannot compute dim(T()) at type definition time, so we use methods instead
+struct Lagrange{T<:AbstractTopology,P} end
+
+# Define interface methods for Lagrange
+# Dimension comes from topology
+Base.ndims(::Type{Lagrange{T,P}}) where {T,P} = dim(T())
+Base.ndims(::Lagrange{T,P}) where {T,P} = dim(T())
+
+# Node count formulas for different topologies and polynomial degrees
+# These replace the hardcoded node counts in old Tri3, Quad4, etc. types
+
+"""
+    nnodes(::Lagrange{T, P}) where {T, P}
+
+Compute number of nodes for Lagrange basis of degree P on topology T.
+"""
+# 1D: Segment
+nnodes(::Lagrange{Segment,P}) where {P} = P + 1
+
+# 2D: Triangle (simplex)
+nnodes(::Lagrange{Triangle,P}) where {P} = div((P + 1) * (P + 2), 2)
+
+# 2D: Quadrilateral (tensor product)
+nnodes(::Lagrange{Quadrilateral,P}) where {P} = (P + 1)^2
+
+# 3D: Tetrahedron (simplex)
+nnodes(::Lagrange{Tetrahedron,P}) where {P} = div((P + 1) * (P + 2) * (P + 3), 6)
+
+# 3D: Hexahedron (tensor product)
+nnodes(::Lagrange{Hexahedron,P}) where {P} = (P + 1)^3
+
+# 3D: Pyramid (mixed)
+# Pyramids don't follow a simple formula, so hardcode for known degrees
+nnodes(::Lagrange{Pyramid,1}) = 5
+nnodes(::Lagrange{Pyramid,2}) = 13
+nnodes(::Lagrange{Pyramid,3}) = 29
+
+# 3D: Wedge/Prism (triangle × segment tensor product)
+nnodes(::Lagrange{Wedge,P}) where {P} = div((P + 1)^2 * (P + 2), 2)
+
+# Export the new parametric type and node count function
+export Lagrange, nnodes