diff --git a/src/pyprojroot/root.py b/src/pyprojroot/root.py
index d2a5377..2260764 100644
--- a/src/pyprojroot/root.py
+++ b/src/pyprojroot/root.py
@@ -6,7 +6,7 @@
 """
 
 from pathlib import Path
-from typing import Union, Tuple
+from typing import Union, Tuple, Optional
 
 from .criterion import (
     as_root_criterion as _as_root_criterion,
@@ -15,13 +15,11 @@
 )
 
 
-def as_start_path(start: Union[None, _PathType]) -> Path:
-    if start is None:
-        return Path.cwd()
-    if not isinstance(start, Path):
-        start = Path(start)
-    # TODO: consider `start = start.resolve()`
-    return start
+def as_start_path(start: Optional[_PathType]) -> Path:
+    """Convert path argument into normalised Path object."""
+    if start is not None:
+        return Path(start).expanduser().resolve()
+    return Path.cwd().resolve()
 
 
 def find_root_with_reason(
@@ -39,7 +37,6 @@ def find_root_with_reason(
     # Prepare inputs
     criterion = _as_root_criterion(criterion)
     start = as_start_path(start)
-
     # Check start
     if start.is_dir() and criterion(start):
         return start, "Pass"
diff --git a/tests/test_root.py b/tests/test_root.py
new file mode 100644
index 0000000..17b0e58
--- /dev/null
+++ b/tests/test_root.py
@@ -0,0 +1,60 @@
+import os
+
+import pytest
+
+from pyprojroot.root import as_start_path, find_root
+
+MARKER = ".here"
+
+
+@pytest.fixture
+def temp_dir_structure(tmp_path):
+    """
+    Create a pytest temp path for testing:
+
+    tmp_path/
+    └── dir1/
+        ├── .here  <-- marker file
+        └── dir2/
+    """
+    dir1 = tmp_path / "dir1"
+    dir2 = dir1 / "dir2"
+    os.makedirs(dir1 / MARKER)
+    os.makedirs(dir2)
+    return dir1, dir2
+
+
+def test_as_start_path_normalized_path():
+    result01 = as_start_path("~")  # Home
+    assert result01.is_dir()
+
+    result02 = as_start_path("~/.")  # Still at Home
+    assert result02.is_dir()
+    assert result01 == result02
+
+    result03 = as_start_path("~/..")  # One directory below Home
+    assert result03.is_dir()
+    assert result03 != result02
+
+
+def test_find_root_marker_in_child(temp_dir_structure):
+    """Marker is in child folder, checking the parent should raise."""
+    dir1, _ = temp_dir_structure
+
+    os.chdir(dir1)
+    result = find_root(MARKER, start=".")
+    assert result.is_dir()
+
+    with pytest.raises(RuntimeError, match="Project root not found."):
+        find_root(MARKER, start="..")
+
+
+def test_find_root_marker_in_parent(temp_dir_structure):
+    """Marker in parent - child and parent should successfully find a root."""
+    _, dir2 = temp_dir_structure
+    os.chdir(dir2)
+    result01 = find_root(MARKER, start=".")
+    assert result01.is_dir()
+
+    result02 = find_root(MARKER, start="..")
+    assert result02.is_dir()