diff --git a/README.md b/README.md
index ea40b37..0d54a8d 100644
--- a/README.md
+++ b/README.md
@@ -11,8 +11,10 @@ is a simple file path library for Carp.
 ### Usage
 
 The `Path` module mostly operates on `String` arguments. It allows you to
-split, join, and merge paths and extensions in a lot of different ways. It also
-has some functions to work with the `PATH` environment variable.
+split, join, merge, and normalize paths and extensions in a lot of different
+ways. `normalize` resolves `.`/`..` segments and collapses repeated separators
+lexically (without touching the filesystem). It also has some functions to work
+with the `PATH` environment variable.
 
 It assumes either Windows or POSIX-style separators.
 
diff --git a/path.carp b/path.carp
index a6fa099..6c87314 100644
--- a/path.carp
+++ b/path.carp
@@ -89,6 +89,53 @@ Otherwise returns `Just` of the last component.")
           but-last (Array.prefix &split (dec (Array.length &split)))]
       (String.join sep-string &but-last)))
 
+  (doc normalize "normalizes the path `p` lexically, without touching the
+filesystem.
+
+It collapses repeated separators, drops `.` components, and resolves each `..`
+against the preceding component. Leading `..` components are kept in relative
+paths (they cannot be resolved without a base), and `..` never escapes the root
+of an absolute path. An empty or fully-cancelling relative path normalizes to
+`.`, and a fully-cancelling absolute path normalizes to its root (a lone
+separator on POSIX, the drive root such as `C:\\` on Windows).
+
+Examples on POSIX:
+```
+(normalize \"a/./b\")    ; => \"a/b\"
+(normalize \"a/b/../c\") ; => \"a/c\"
+(normalize \"//a///b\")  ; => \"/a/b\"
+(normalize \"/a/../..\") ; => \"/\"
+(normalize \"a/../..\")  ; => \"..\"
+(normalize \"\")         ; => \".\"
+```")
+  (defn normalize [p]
+    (if (String.empty? p)
+      @"."
+      (let-do [abs (absolute? p)
+               comps (split p)
+               out []]
+        ; on an absolute path the first component is the root marker — "" on
+        ; POSIX, the drive (e.g. "C:") on Windows — so skip it here and re-attach
+        ; it verbatim below: that preserves the drive and stops `..` escaping root
+        (for [i (if abs 1 0) (Array.length &comps)]
+          (let [c (Array.unsafe-nth &comps i)]
+            (cond
+              (or (String.empty? c) (= c ".")) ()
+              (= c "..")
+                (let [n (Array.length &out)]
+                  (cond
+                    (= n 0) (unless abs (set! out (Array.push-back out @c)))
+                    (= (Array.unsafe-nth &out (dec n)) "..")
+                      (set! out (Array.push-back out @c))
+                    (set! out (Array.prefix &out (dec n)))))
+              (set! out (Array.push-back out @c)))))
+        (let [joined (String.join sep-string &out)]
+          (cond
+            abs
+              (String.concat &[@(Array.unsafe-nth &comps 0) @sep-string joined])
+            (String.empty? &joined) @"."
+            joined)))))
+
   (doc split-extension "splits the path `p` on its extension.
 
 It will return a `(Maybe (Pair String String))`. `Maybe` because there might not
diff --git a/test/path.carp b/test/path.carp
index adbc29c..b34f843 100644
--- a/test/path.carp
+++ b/test/path.carp
@@ -60,6 +60,37 @@
       "path/to/file"
       &(join &[@"path" @"to" @"file"])
       "join works")
+    (assert-equal test "a/b" &(normalize "a/./b") "normalize drops . components")
+    (assert-equal test "a/c" &(normalize "a/b/../c") "normalize resolves ..")
+    (assert-equal test
+      "/a/b"
+      &(normalize "//a///b")
+      "normalize collapses repeated separators")
+    (assert-equal test
+      "/"
+      &(normalize "/a/../..")
+      "normalize keeps absolute .. from escaping root")
+    (assert-equal test "/" &(normalize "/") "normalize keeps the root")
+    (assert-equal test
+      ".."
+      &(normalize "a/../..")
+      "normalize keeps a leading .. in a relative path")
+    (assert-equal test
+      "../b"
+      &(normalize "../a/../b")
+      "normalize preserves unresolvable leading ..")
+    (assert-equal test
+      "."
+      &(normalize "")
+      "normalize turns the empty path into .")
+    (assert-equal test
+      "."
+      &(normalize "a/b/../..")
+      "normalize turns a fully-cancelling relative path into .")
+    (assert-equal test
+      "a"
+      &(normalize "a/")
+      "normalize strips a trailing separator")
     (assert-equal test
       &(Maybe.Just @"file.txt")
       &(filename "path/to/file.txt")