**Table of Contents**

- Basic Operations
- Interpolation
- Data Levelling and Background Subtraction
- Masks
- Filters
- Presentations
- Scan Line Artefacts
- Local Defects
- Global Distortions
- Statistical Analysis
- One-Dimensional Roughness Parameters
- Feature Measurement
- Grain Analysis
- Fourier Transform
- Wavelet Transform
- Fractal Analysis
- Tip Convolution Artefacts
- Force and Indentation
- Convolution and deconvolution
- Multiple Data
- Magnetic force microscopy
- Scanning Microwave Microscopy
- Graph Processing
- Volume Data Processing
- Volume Data Processing: Image stacks
- XYZ Data Processing
- Curve Maps Data Processing
- Force Distance Curve Maps
- Synthetic Surfaces
- Calibration and uncertainties
- Python Scripting
- Plug-ins

The number and breadth of data manipulation and analysis functions is one of the Gwyddion main strengths. The description of their principles and applications is the purpose of this chapter, with focus on the explanation of how they work and what they calculate or perform. Elements of their user interface are also occasionally described where it seems useful, nevertheless, it is assumed the reader is familiar with the basic organization of data and controls in Gwyddion, as described in the previous chapter.