Further reading
This page names what the volume declined, and why, so that a reader knows where its edges are rather than discovering them.
Read the paper
Before anything else. The German original is public domain, is freely available online in a transcription proofread against the source, and carries its mathematics intact — which was not true for most of the period during which the textbook version of "Noether's theorem" formed.
It is twenty-three pages in six sections. A guide to reading it in its own order is in this volume.
The English translations are all under copyright, and this volume quotes none of them. If you read English only, the paper is still worth having beside a translation you obtain elsewhere, because the equations are legible in any language.
What this volume does not derive
Each item below is discussed somewhere in the volume, marked as underived, and would need a text of its own.
Lie theory proper. The classification of continuous groups. Neither theorem needs it; the Lie page carries only the commutator and the closure condition.
Jet bundles and the variational bicomplex. The modern framework in which both theorems are corollaries of a statement about a differential complex. Noether proves both without it. Discussion, or in plain language.
The general moment map. Existence, equivariance, and the relation to the Lie algebra's structure. Two cases are checked in this volume and the general construction is not. Discussion, or in plain language.
Quantum field theory. The Ward-Takahashi identity and the anomaly are named, their shape is described, and neither is derived. This is the ceiling of the volume. Discussion, or in plain language.
The Belinfante construction. Why the improvement is permitted is derived here; that a symmetrising choice always exists is not. Discussion, or in plain language.
The symmetry behind the Runge-Lenz vector. The conserved quantity is exhibited and checked; the symmetry is not. Discussion.
Open questions this volume leaves
Which precursor anticipated what. Noether names eight people. Measuring what each of them established, and under what restriction, requires reading eight papers against her two theorems. No priority verdict is made or implied. Discussion.
How the paper was actually received between 1918 and 1960. No citation trace was performed. The usual explanations are recorded as claims. Discussion.
Which theorem Kelvin's circulation theorem belongs to. The symmetry is a free shape, which puts it on the second theorem's side, and the derivation that would settle it was not done. Discussion.
For the mathematics without the history
Any graduate text on classical field theory carries the first theorem in its field-theory special case. Be aware, reading one, of the four things that version usually drops: the second theorem, both converses, the general derivative order, and the correct attribution of divergence invariance. The page on the recovery explains how each was lost.